TCS Wiki - User contributions [en]

数据科学基础 (Fall 2024)/第六次作业提交名单

2024-12-29T10:12:57Z

Zhoucan:

<center>
{| class="wikitable"
|-
! 学号
|-
| 221850088
|-
| 221870109
|-
| 221900009
|-
| 221900024
|-
| 221900028
|-
| 221900029
|-
| 221900036
|-
| 221900038
|-
| 221900042
|-
| 221900055
|-
| 221900068
|-
| 221900073
|-
| 221900075
|-
| 221900083
|-
| 221900084
|-
| 221900085
|-
| 221900091
|-
| 221900124
|-
| 221900128
|-
| 221900140
|-
| 221900159
|-
| 221900168
|-
| 221900183
|-
| 221900208
|-
| 221900209
|-
| 221900210
|-
| 221900216
|-
| 221900223
|-
| 221900230
|-
| 221900234
|-
| 221900246
|-
| 221900263
|-
| 221900264
|-
| 221900268
|-
| 221900270
|-
| 221900277
|-
| 221900309
|-
| 221900311
|-
| 221900318
|-
| 221900320
|-
| 221900323
|-
| 221900324
|-
| 221900325
|-
| 221900326
|-
| 221900328
|-
| 221900339
|-
| 221900342
|-
| 221900346
|-
| 221900347
|-
| 221900353
|-
| 221900362
|-
| 221900371
|-
| 221900375
|-
| 221900379
|-
| 221900387
|-
| 221900406
|-
| 221900418
|-
| 221900426
|-
| 221900431
|-
| 221900450
|-
| 221900455
|-
| 221900461
|-
| 221900477
|-
| 221900490
|-
| 221900497
|-
| 231170041
|-
| 231880007
|-
| 231880027
|-
| 231880042
|-
| 231880076
|-
| 231880078
|-
| 231880087
|-
| 231880092
|-
| 231880099
|-
| 231880102
|-
| 231880167
|-
| 231880224
|-
| 231880292
|-
| 231880313
|-
| 231880316
|-
| 231880324
|-
| 231880340
|-
| 231880357
|-
| 231880367
|-
| 231880382
|-
| 231880403
|-
| 231880410
|-
| 231880423
|-
| 231880426
|-
| 231880429
|-
| 231880443
|-
| 231880481
|-
| 231880498
|-
| 231880513
|-
| 231880514
|-
| 231880515
|}
</center>

数据科学基础 (Fall 2024)/第六次作业提交名单

2024-12-27T04:25:32Z

Zhoucan:

<center>
{| class="wikitable"
|-
! 学号
|-
| 221850088
|-
| 221870109
|-
| 221900009
|-
| 221900024
|-
| 221900028
|-
| 221900029
|-
| 221900036
|-
| 221900038
|-
| 221900042
|-
| 221900055
|-
| 221900068
|-
| 221900073
|-
| 221900075
|-
| 221900083
|-
| 221900084
|-
| 221900085
|-
| 221900091
|-
| 221900124
|-
| 221900128
|-
| 221900140
|-
| 221900159
|-
| 221900168
|-
| 221900183
|-
| 221900208
|-
| 221900209
|-
| 221900210
|-
| 221900216
|-
| 221900223
|-
| 221900230
|-
| 221900234
|-
| 221900246
|-
| 221900263
|-
| 221900264
|-
| 221900268
|-
| 221900270
|-
| 221900277
|-
| 221900309
|-
| 221900311
|-
| 221900318
|-
| 221900320
|-
| 221900323
|-
| 221900324
|-
| 221900325
|-
| 221900326
|-
| 221900328
|-
| 221900339
|-
| 221900342
|-
| 221900346
|-
| 221900347
|-
| 221900353
|-
| 221900362
|-
| 221900371
|-
| 221900375
|-
| 221900379
|-
| 221900387
|-
| 221900406
|-
| 221900418
|-
| 221900426
|-
| 221900431
|-
| 221900450
|-
| 221900455
|-
| 221900461
|-
| 221900477
|-
| 221900490
|-
| 221900497
|-
| 231170041
|-
| 231880007
|-
| 231880027
|-
| 231880042
|-
| 231880076
|-
| 231880078
|-
| 231880087
|-
| 231880092
|-
| 231880099
|-
| 231880102
|-
| 231880167
|-
| 231880292
|-
| 231880313
|-
| 231880316
|-
| 231880324
|-
| 231880340
|-
| 231880357
|-
| 231880367
|-
| 231880382
|-
| 231880403
|-
| 231880410
|-
| 231880423
|-
| 231880426
|-
| 231880429
|-
| 231880443
|-
| 231880481
|-
| 231880498
|-
| 231880513
|-
| 231880514
|-
| 231880515
|}
</center>

数据科学基础 (Fall 2024)/第六次作业提交名单

2024-12-25T05:11:47Z

Zhoucan:

<center>
{| class="wikitable"
|-
! 学号
|-
| 221850088
|-
| 221870109
|-
| 221900009
|-
| 221900024
|-
| 221900028
|-
| 221900029
|-
| 221900036
|-
| 221900038
|-
| 221900042
|-
| 221900055
|-
| 221900068
|-
| 221900073
|-
| 221900075
|-
| 221900083
|-
| 221900084
|-
| 221900085
|-
| 221900091
|-
| 221900124
|-
| 221900128
|-
| 221900140
|-
| 221900159
|-
| 221900168
|-
| 221900183
|-
| 221900208
|-
| 221900209
|-
| 221900210
|-
| 221900216
|-
| 221900223
|-
| 221900230
|-
| 221900234
|-
| 221900246
|-
| 221900263
|-
| 221900264
|-
| 221900268
|-
| 221900270
|-
| 221900277
|-
| 221900309
|-
| 221900311
|-
| 221900320
|-
| 221900323
|-
| 221900324
|-
| 221900325
|-
| 221900326
|-
| 221900328
|-
| 221900339
|-
| 221900342
|-
| 221900346
|-
| 221900347
|-
| 221900353
|-
| 221900362
|-
| 221900371
|-
| 221900375
|-
| 221900379
|-
| 221900387
|-
| 221900406
|-
| 221900418
|-
| 221900426
|-
| 221900431
|-
| 221900450
|-
| 221900455
|-
| 221900461
|-
| 221900477
|-
| 221900490
|-
| 221900497
|-
| 231170041
|-
| 231880007
|-
| 231880027
|-
| 231880042
|-
| 231880076
|-
| 231880078
|-
| 231880087
|-
| 231880092
|-
| 231880099
|-
| 231880102
|-
| 231880167
|-
| 231880292
|-
| 231880313
|-
| 231880316
|-
| 231880324
|-
| 231880340
|-
| 231880357
|-
| 231880367
|-
| 231880382
|-
| 231880403
|-
| 231880410
|-
| 231880423
|-
| 231880426
|-
| 231880429
|-
| 231880443
|-
| 231880481
|-
| 231880498
|-
| 231880513
|-
| 231880514
|-
| 231880515
|}
</center>

数据科学基础 (Fall 2024)/第五次作业提交名单

2024-12-20T05:54:48Z

Zhoucan:

<center>
{| class="wikitable"
|-
! 学号
|-
| 221850088
|-
| 221870109
|-
| 221900009
|-
| 221900024
|-
| 221900028
|-
| 221900029
|-
| 221900036
|-
| 221900038
|-
| 221900042
|-
| 221900046
|-
| 221900055
|-
| 221900073
|-
| 221900075
|-
| 221900083
|-
| 221900084
|-
| 221900085
|-
| 221900091
|-
| 221900124
|-
| 221900128
|-
| 221900140
|-
| 221900159
|-
| 221900168
|-
| 221900183
|-
| 221900187
|-
| 221900208
|-
| 221900209
|-
| 221900210
|-
| 221900216
|-
| 221900223
|-
| 221900230
|-
| 221900234
|-
| 221900246
|-
| 221900263
|-
| 221900264
|-
| 221900268
|-
| 221900270
|-
| 221900277
|-
| 221900309
|-
| 221900311
|-
| 221900318
|-
| 221900320
|-
| 221900323
|-
| 221900324
|-
| 221900325
|-
| 221900326
|-
| 221900328
|-
| 221900339
|-
| 221900342
|-
| 221900346
|-
| 221900347
|-
| 221900353
|-
| 221900362
|-
| 221900371
|-
| 221900375
|-
| 221900379
|-
| 221900387
|-
| 221900406
|-
| 221900418
|-
| 221900425
|-
| 221900426
|-
| 221900431
|-
| 221900450
|-
| 221900455
|-
| 221900461
|-
| 221900477
|-
| 221900490
|-
| 221900497
|-
| 231170041
|-
| 231880007
|-
| 231880027
|-
| 231880042
|-
| 231880076
|-
| 231880087
|-
| 231880092
|-
| 231880099
|-
| 231880102
|-
| 231880224
|-
| 231880292
|-
| 231880313
|-
| 231880316
|-
| 231880324
|-
| 231880340
|-
| 231880357
|-
| 231880367
|-
| 231880382
|-
| 231880403
|-
| 231880410
|-
| 231880423
|-
| 231880426
|-
| 231880429
|-
| 231880443
|-
| 231880481
|-
| 231880498
|-
| 231880513
|-
| 231880514
|-
| 231880515
|}
</center>

数据科学基础 (Fall 2024)/第五次作业提交名单

2024-12-19T06:39:27Z

Zhoucan:

<center>
{| class="wikitable"
|-
! 学号
|-
| 23188078
|-
| 221850088
|-
| 221870109
|-
| 221900009
|-
| 221900024
|-
| 221900028
|-
| 221900029
|-
| 221900038
|-
| 221900042
|-
| 221900046
|-
| 221900055
|-
| 221900073
|-
| 221900075
|-
| 221900083
|-
| 221900084
|-
| 221900085
|-
| 221900091
|-
| 221900124
|-
| 221900128
|-
| 221900140
|-
| 221900159
|-
| 221900168
|-
| 221900183
|-
| 221900187
|-
| 221900208
|-
| 221900209
|-
| 221900210
|-
| 221900216
|-
| 221900223
|-
| 221900230
|-
| 221900234
|-
| 221900246
|-
| 221900263
|-
| 221900264
|-
| 221900268
|-
| 221900270
|-
| 221900277
|-
| 221900309
|-
| 221900311
|-
| 221900320
|-
| 221900323
|-
| 221900324
|-
| 221900325
|-
| 221900326
|-
| 221900328
|-
| 221900339
|-
| 221900342
|-
| 221900346
|-
| 221900347
|-
| 221900353
|-
| 221900362
|-
| 221900371
|-
| 221900375
|-
| 221900379
|-
| 221900387
|-
| 221900406
|-
| 221900418
|-
| 221900425
|-
| 221900426
|-
| 221900431
|-
| 221900450
|-
| 221900455
|-
| 221900461
|-
| 221900477
|-
| 221900490
|-
| 221900497
|-
| 231170041
|-
| 231880007
|-
| 231880027
|-
| 231880042
|-
| 231880076
|-
| 231880087
|-
| 231880092
|-
| 231880099
|-
| 231880102
|-
| 231880224
|-
| 231880292
|-
| 231880313
|-
| 231880316
|-
| 231880324
|-
| 231880340
|-
| 231880357
|-
| 231880367
|-
| 231880382
|-
| 231880403
|-
| 231880410
|-
| 231880423
|-
| 231880426
|-
| 231880429
|-
| 231880443
|-
| 231880481
|-
| 231880498
|-
| 231880513
|-
| 231880514
|-
| 231880515
|}
</center>

数据科学基础 (Fall 2024)/第四次作业提交名单

2024-11-21T16:24:06Z

Zhoucan:

<center>
{| class="wikitable"
|-
! 学号
|-
| 221850088
|-
| 221870109
|-
| 221900009
|-
| 221900024
|-
| 221900028
|-
| 221900029
|-
| 221900036
|-
| 221900038
|-
| 221900042
|-
| 221900046
|-
| 221900055
|-
| 221900068
|-
| 221900073
|-
| 221900075
|-
| 221900083
|-
| 221900084
|-
| 221900085
|-
| 221900091
|-
| 221900124
|-
| 221900128
|-
| 221900140
|-
| 221900159
|-
| 221900168
|-
| 221900183
|-
| 221900208
|-
| 221900209
|-
| 221900210
|-
| 221900216
|-
| 221900223
|-
| 221900230
|-
| 221900234
|-
| 221900246
|-
| 221900263
|-
| 221900264
|-
| 221900268
|-
| 221900270
|-
| 221900277
|-
| 221900309
|-
| 221900311
|-
| 221900318
|-
| 221900320
|-
| 221900323
|-
| 221900324
|-
| 221900325
|-
| 221900326
|-
| 221900328
|-
| 221900339
|-
| 221900342
|-
| 221900346
|-
| 221900347
|-
| 221900353
|-
| 221900362
|-
| 221900371
|-
| 221900375
|-
| 221900379
|-
| 221900387
|-
| 221900406
|-
| 221900418
|-
| 221900425
|-
| 221900426
|-
| 221900450
|-
| 221900455
|-
| 221900461
|-
| 221900477
|-
| 221900490
|-
| 221900497
|-
| 231170041
|-
| 231880007
|-
| 231880027
|-
| 231880042
|-
| 231880076
|-
| 231880078
|-
| 231880087
|-
| 231880092
|-
| 231880099
|-
| 231880102
|-
| 231880167
|-
| 231880224
|-
| 231880292
|-
| 231880313
|-
| 231880316
|-
| 231880324
|-
| 231880340
|-
| 231880357
|-
| 231880367
|-
| 231880382
|-
| 231880403
|-
| 231880410
|-
| 231880423
|-
| 231880426
|-
| 231880429
|-
| 231880443
|-
| 231880481
|-
| 231880498
|-
| 231880513
|-
| 231880514
|-
| 231880515
|}
</center>

数据科学基础 (Fall 2024)/第四次作业提交名单

2024-11-21T08:09:51Z

Zhoucan:

<center>
{| class="wikitable"
|-
! 学号
|-
| 221850088
|-
| 221870109
|-
| 221900009
|-
| 221900024
|-
| 221900028
|-
| 221900029
|-
| 221900036
|-
| 221900038
|-
| 221900042
|-
| 221900046
|-
| 221900055
|-
| 221900068
|-
| 221900073
|-
| 221900075
|-
| 221900083
|-
| 221900084
|-
| 221900085
|-
| 221900091
|-
| 221900124
|-
| 221900128
|-
| 221900140
|-
| 221900159
|-
| 221900168
|-
| 221900183
|-
| 221900208
|-
| 221900209
|-
| 221900210
|-
| 221900216
|-
| 221900223
|-
| 221900230
|-
| 221900234
|-
| 221900246
|-
| 221900263
|-
| 221900264
|-
| 221900268
|-
| 221900270
|-
| 221900277
|-
| 221900309
|-
| 221900311
|-
| 221900318
|-
| 221900320
|-
| 221900323
|-
| 221900324
|-
| 221900325
|-
| 221900326
|-
| 221900328
|-
| 221900339
|-
| 221900342
|-
| 221900346
|-
| 221900347
|-
| 221900353
|-
| 221900362
|-
| 221900371
|-
| 221900375
|-
| 221900379
|-
| 221900387
|-
| 221900406
|-
| 221900418
|-
| 221900425
|-
| 221900426
|-
| 221900450
|-
| 221900455
|-
| 221900461
|-
| 221900477
|-
| 221900490
|-
| 221900497
|-
| 231170041
|-
| 231880007
|-
| 231880027
|-
| 231880042
|-
| 231880076
|-
| 231880078
|-
| 231880087
|-
| 231880092
|-
| 231880099
|-
| 231880102
|-
| 231880167
|-
| 231880224
|-
| 231880292
|-
| 231880313
|-
| 231880316
|-
| 231880324
|-
| 231880357
|-
| 231880367
|-
| 231880382
|-
| 231880403
|-
| 231880410
|-
| 231880423
|-
| 231880426
|-
| 231880429
|-
| 231880443
|-
| 231880481
|-
| 231880498
|-
| 231880513
|-
| 231880514
|-
| 231880515
|}
</center>

数据科学基础 (Fall 2024)/第三次作业提交名单

2024-11-05T02:18:14Z

Zhoucan:

<center>
{| class="wikitable"
|-
! 学号
|-
| 221850088
|-
| 221870109
|-
| 221900009
|-
| 221900028
|-
| 221900029
|-
| 221900036
|-
| 221900038
|-
| 221900042
|-
| 221900046
|-
| 221900055
|-
| 221900068
|-
| 221900073
|-
| 221900075
|-
| 221900083
|-
| 221900084
|-
| 221900085
|-
| 221900091
|-
| 221900124
|-
| 221900128
|-
| 221900140
|-
| 221900159
|-
| 221900168
|-
| 221900183
|-
| 221900187
|-
| 221900208
|-
| 221900209
|-
| 221900210
|-
| 221900216
|-
| 221900223
|-
| 221900230
|-
| 221900234
|-
| 221900246
|-
| 221900263
|-
| 221900264
|-
| 221900268
|-
| 221900270
|-
| 221900277
|-
| 221900309
|-
| 221900311
|-
| 221900318
|-
| 221900320
|-
| 221900323
|-
| 221900324
|-
| 221900325
|-
| 221900326
|-
| 221900328
|-
| 221900339
|-
| 221900342
|-
| 221900346
|-
| 221900347
|-
| 221900353
|-
| 221900362
|-
| 221900371
|-
| 221900375
|-
| 221900379
|-
| 221900387
|-
| 221900406
|-
| 221900418
|-
| 221900425
|-
| 221900426
|-
| 221900431
|-
| 221900450
|-
| 221900455
|-
| 221900461
|-
| 221900477
|-
| 221900490
|-
| 231170041
|-
| 231880007
|-
| 231880027
|-
| 231880042
|-
| 231880072
|-
| 231880076
|-
| 231880078
|-
| 231880087
|-
| 231880092
|-
| 231880099
|-
| 231880102
|-
| 231880167
|-
| 231880224
|-
| 231880292
|-
| 231880313
|-
| 231880316
|-
| 231880324
|-
| 231880340
|-
| 231880357
|-
| 231880367
|-
| 231880382
|-
| 231880403
|-
| 231880410
|-
| 231880423
|-
| 231880426
|-
| 231880429
|-
| 231880443
|-
| 231880481
|-
| 231880498
|-
| 231880513
|-
| 231880514
|-
| 231880515
|}
</center>

数据科学基础 (Fall 2024)/第二次作业提交名单

2024-10-28T06:09:16Z

Zhoucan:

<center>
{| class="wikitable"
|-
! 学号
|-
| 221850088
|-
| 221870109
|-
| 221900009
|-
| 221900024
|-
| 221900028
|-
| 221900029
|-
| 221900036
|-
| 221900038
|-
| 221900042
|-
| 221900046
|-
| 221900055
|-
| 221900068
|-
| 221900073
|-
| 221900075
|-
| 221900076
|-
| 221900083
|-
| 221900084
|-
| 221900085
|-
| 221900091
|-
| 221900124
|-
| 221900128
|-
| 221900140
|-
| 221900159
|-
| 221900168
|-
| 221900175
|-
| 221900183
|-
| 221900187
|-
| 221900208
|-
| 221900209
|-
| 221900210
|-
| 221900216
|-
| 221900220
|-
| 221900223
|-
| 221900230
|-
| 221900234
|-
| 221900246
|-
| 221900263
|-
| 221900264
|-
| 221900268
|-
| 221900270
|-
| 221900277
|-
| 221900309
|-
| 221900311
|-
| 221900318
|-
| 221900320
|-
| 221900323
|-
| 221900324
|-
| 221900325
|-
| 221900326
|-
| 221900328
|-
| 221900339
|-
| 221900342
|-
| 221900346
|-
| 221900347
|-
| 221900353
|-
| 221900362
|-
| 221900371
|-
| 221900375
|-
| 221900379
|-
| 221900387
|-
| 221900406
|-
| 221900418
|-
| 221900425
|-
| 221900426
|-
| 221900431
|-
| 221900450
|-
| 221900455
|-
| 221900461
|-
| 221900477
|-
| 221900490
|-
| 221900497
|-
| 231170041
|-
| 231830131
|-
| 231880007
|-
| 231880027
|-
| 231880042
|-
| 231880072
|-
| 231880076
|-
| 231880078
|-
| 231880087
|-
| 231880092
|-
| 231880099
|-
| 231880102
|-
| 231880167
|-
| 231880184
|-
| 231880185
|-
| 231880199
|-
| 231880224
|-
| 231880245
|-
| 231880255
|-
| 231880280
|-
| 231880292
|-
| 231880313
|-
| 231880316
|-
| 231880324
|-
| 231880340
|-
| 231880357
|-
| 231880367
|-
| 231880382
|-
| 231880403
|-
| 231880410
|-
| 231880423
|-
| 231880426
|-
| 231880429
|-
| 231880439
|-
| 231880443
|-
| 231880472
|-
| 231880474
|-
| 231880481
|-
| 231880498
|-
| 231880513
|-
| 231880514
|-
| 231880515
|}
</center>

数据科学基础 (Fall 2024)/第二次作业提交名单

2024-10-27T10:54:23Z

Zhoucan: 去重

<center>
{| class="wikitable"
|-
! 学号
|-
| 221850088
|-
| 221870109
|-
| 221900009
|-
| 221900024
|-
| 221900028
|-
| 221900029
|-
| 221900036
|-
| 221900038
|-
| 221900042
|-
| 221900046
|-
| 221900055
|-
| 221900068
|-
| 221900073
|-
| 221900075
|-
| 221900076
|-
| 221900083
|-
| 221900084
|-
| 221900085
|-
| 221900091
|-
| 221900124
|-
| 221900128
|-
| 221900140
|-
| 221900159
|-
| 221900168
|-
| 221900175
|-
| 221900183
|-
| 221900187
|-
| 221900208
|-
| 221900209
|-
| 221900210
|-
| 221900216
|-
| 221900220
|-
| 221900223
|-
| 221900230
|-
| 221900234
|-
| 221900246
|-
| 221900263
|-
| 221900264
|-
| 221900268
|-
| 221900270
|-
| 221900309
|-
| 221900311
|-
| 221900318
|-
| 221900320
|-
| 221900323
|-
| 221900324
|-
| 221900325
|-
| 221900326
|-
| 221900328
|-
| 221900339
|-
| 221900342
|-
| 221900346
|-
| 221900347
|-
| 221900353
|-
| 221900362
|-
| 221900371
|-
| 221900375
|-
| 221900379
|-
| 221900387
|-
| 221900406
|-
| 221900418
|-
| 221900425
|-
| 221900426
|-
| 221900431
|-
| 221900450
|-
| 221900455
|-
| 221900461
|-
| 221900477
|-
| 221900490
|-
| 221900497
|-
| 231170041
|-
| 231830131
|-
| 231880007
|-
| 231880027
|-
| 231880042
|-
| 231880072
|-
| 231880076
|-
| 231880078
|-
| 231880087
|-
| 231880092
|-
| 231880099
|-
| 231880102
|-
| 231880167
|-
| 231880184
|-
| 231880185
|-
| 231880199
|-
| 231880224
|-
| 231880245
|-
| 231880255
|-
| 231880280
|-
| 231880292
|-
| 231880313
|-
| 231880316
|-
| 231880324
|-
| 231880340
|-
| 231880357
|-
| 231880367
|-
| 231880382
|-
| 231880410
|-
| 231880423
|-
| 231880426
|-
| 231880429
|-
| 231880439
|-
| 231880443
|-
| 231880472
|-
| 231880474
|-
| 231880481
|-
| 231880498
|-
| 231880513
|-
| 231880514
|-
| 231880515
|}
</center>

数据科学基础 (Fall 2024)/Problem Set 4

2024-10-26T09:51:33Z

Zhoucan:

*每道题目的解答都要有完整的解题过程，中英文不限。

*我们推荐大家使用LaTeX, markdown等对作业进行排版。

*没有条件的同学可以用纸笔完成作业之后拍照。

== Assumption throughout Problem Set 4 ==
<p>Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\Pr)</math>.</p>

<p>Without further notice, we assume that the expectation of random variables are well-defined.</p>

== Problem 1 (Moments and (co)variances) ==
* ['''Run (ii)'''] A biased coin is tossed <math>n</math> times, and heads shows with probability <math>p</math> on each toss. A run is a sequence of throws which result in the same outcome, so that, for example, the sequence HHTHTTH contains five runs.
<ol>
<li>Find the variance of the number of runs.
</li><li>Let <math>h</math> heads and <math>t</math> tails be arranged randomly in a line. Find the mean and variance of the number of runs of heads.
</li>
</ol>
* ['''Random sum (ii)'''] Let <math>S= \sum^N_{i=1} X_i</math> , where the <math>X_i, i \ge 1,</math> are independent, identically distributed random variables with mean <math>\mu</math> and variance <math>\sigma^2</math>, and <math>N</math> is positive, integer-valued, and independent of the <math>X_i</math> . Show that <math>\mathrm{Var}(S)= \sigma^2\cdot\mathbb E[N]+ \mu^2\cdot\mathrm{Var}(N)</math>.
* ['''Maximum variance'''] Let <math>X_1,X_2,...,X_n</math> be independent random variables, and suppose that <math>X_k</math> is Bernoulli with parameter <math>p_k</math> . Show that <math>Y= X_1 + X_2 + \dots + X_n</math> has mean and variance given by <math>\mathbb E[Y ]= \sum^n_1 p_k , \mathrm{Var}(Y )= \sum^n_1 p_k (1− p_k )</math>. Show that, for <math>\mathbb E[Y]</math> fixed, <math>\mathrm{Var}(Y )</math> is a maximum when <math>p_1 = p_2 = \dots = p_n</math>. That is to say, the variation in the sum is greatest when individuals are most alike. Is this contrary to intuition?
* ['''Moments (i)'''] Let <math>X</math> have mass function
::<math>f(x)=\begin{cases}1/(x(x+1)) & \text{if }x=1,2,\dots,\\ 0 &\text{otherwise,}\end{cases}</math>
:: and let <math>\alpha\ge\mathbb R</math>. For what values of <math>\alpha</math> is it the case that <math>\mathbb E[X^\alpha]<\infty</math>?
* ['''Moments (ii)'''] Let <math>X\sim \text{Geo}(p)</math> for some <math>p \in (0,1)</math>. Find <math>\mathbb{E}[X^3]</math> and <math>\mathbb{E}[X^4]</math>.
* ['''Covariance and correlation (i)'''] Let <math>X</math> and <math>Y</math> be discrete random variables with correlation <math>\rho</math>. Show that <math>|\rho|= 1</math> if and only if <math>X=aY+b</math> for some real numbers <math>a,b</math>.
* ['''Covariance and correlation (ii)''']Let <math>X, Y , Z</math> be non-degenerate and independent random variables. By considering <math>U= X + Y , V= Y + Z, W= Z− X</math>, or otherwise, show that having positive correlation is not a transitive relation.
* ['''Berkson’s fallacy'''] Any individual in a group <math>G</math> contracts a certain disease <math>C</math> with probability <math>\gamma</math>; such individuals are hospitalized with probability <math>c</math>. Independently of this, anyone in <math>G</math> may be in hospital with probability <math>a</math>, for some other reason. Let <math>X</math> be the number in hospital, and <math>Y</math> the number in hospital who have <math>C</math> (including those with <math>C</math> admitted for any other reason). Show that the correlation between <math>X</math> and <math>Y</math> is <math>\rho(X,Y )=\sqrt{\frac{\gamma p}{1-\gamma p}\cdot\frac{(1-a)(1-\gamma c)}{a+\gamma c-a\gamma c}} </math>, where <math>p= a + c− ac</math>. It has been stated erroneously that, when <math>\rho(X,Y )</math> is near unity, this is evidence for a causal relation between being in <math>G</math> and contracting <math>C</math>.
* ['''Correlation and independence'''] Let <math>X</math> and <math>Y</math> be independent Bernoulli random variables with parameter <math>1/2</math> . Show that <math>X + Y</math> and <math>|X− Y |</math> are dependent though uncorrelated.
* ['''Conditional variance formula'''] How should we define <math>\mathrm{Var}(Y | X)</math>, the conditional variance of <math>Y</math> given <math>X</math>? Show that <math>\mathrm{Var}(Y )= \mathbb E[\mathrm{Var}(Y | X)]+ \mathrm{Var}(\mathbb E[Y | X])</math>.
* ['''Conditional covariance'''] Give a definition of the conditional covariance <math>\mathrm{Cov}(X,Y | Z)</math>. Show that <math>\mathrm{Cov}(X,Y )= \mathbb E[ \mathrm{Cov}(X,Y | Z)] + \mathrm{Cov} (\mathbb E[X | Z], \mathbb E[Y | Z])</math> .

== Problem 2 (Markov and Chebyshev) ==
* ['''Markov's inequality'''] Let <math>X</math> be a discrete random variable. Show that for all <math>\beta \geq 0</math> and all <math>x > 0</math>, <math>\Pr[X\geq x]\leq \mathbb{E}[e^{\beta X}]e^{-\beta x}</math>.
* ['''Chebyshev's inequality (i)''' (Cantelli's inequality)] Show that <math>\Pr[X-\mathbb E[X]>t]\le\frac{\mathrm{Var}(X)}{t^2+\mathrm{Var}(X)}, \forall t>0. </math>
* ['''Chebyshev's inequality (ii)''' (Paley–Zygmund inequality)]
# Let <math>X</math> be a random variable with <math>\mathbb E[X]>0</math> and <math>0 <\mathbb E[X^2]<\infty</math>. Show that <math>\Pr[X >a\cdot\mathbb E[X]]\ge \frac{(1− a)^2\cdot \mathbb E[X]^2}{ \mathbb E[X^2]}</math> for <math>0 \le a \le 1</math>.
# Deduce that, if <math>\Pr[X \ge 0]= 1</math>, then <math>\Pr[X= 0]\le\frac{\mathrm{Var}(X)}{\mathbb E[X^2]} \le \frac{\mathrm{Var}(X)}{\mathbb E[X]^2}</math>.
# Let <math>A_1,A_2,\dots,A_n</math> be events, and let <math>X= \sum^n_{r=1} I_{A_r}</math> be the sum of their indicator functions. Show that <math>\Pr[X= 0]\le \frac 1{\mathbb E[X]} + \frac 1 {\mathbb E[X]^2}\sum^∗ \Pr[A_r \cap A_s ]</math>, where the summation <math>\sum^∗</math> is over all distinct unordered pairs <math>r, s</math> such that <math>A_r</math> and <math>A_s</math> are not independent.

== Problem 3 (Random graphs) ==
* ['''Common neighbor'''] Let <math>p \in (0,1)</math> be a constant. Show that with a probability approaching to <math>1</math> (as <math>n</math> tends to infinity) the Erdős–Rényi random graph <math>\mathbf{G}(n,p)</math> has the property that every pair of its vertices has a common neighbor. (Hint: You may use Markov's inequality.)
* ['''Isolated vertices'''] Prove that <math>p = \log n/n</math> is the threshold probability for the disappearance of isolated vertices. Formally, you are required to show that
# with a probability approaching to <math>1</math> (as <math>n</math> tends to infinity) the Erdős–Rényi random graph <math>\mathbf{G} = \mathbf{G}(n,p)</math> has the property that <math>\mathbf{G}</math> has no isolated vertices when <math>p = \omega(\log n/n)</math>;
# with a probability approaching to <math>0</math> (as <math>n</math> tends to infinity) the Erdős–Rényi random graph <math>\mathbf{G} = \mathbf{G}(n,p)</math> has the property that <math>\mathbf{G}</math> has no isolated vertices when <math>p = o(\log n/n)</math>.

数据科学基础 (Fall 2024)/第一次作业提交名单

2024-10-19T08:24:02Z

Zhoucan:

<center>
{| class="wikitable"
|-
! 学号
|-
| 221200004
|-
| 221850088
|-
| 221850088
|-
| 221850088
|-
| 221870109
|-
| 221900009
|-
| 221900024
|-
| 221900028
|-
| 221900029
|-
| 221900036
|-
| 221900038
|-
| 221900042
|-
| 221900046
|-
| 221900055
|-
| 221900068
|-
| 221900073
|-
| 221900075
|-
| 221900076
|-
| 221900083
|-
| 221900084
|-
| 221900085
|-
| 221900091
|-
| 221900091
|-
| 221900124
|-
| 221900128
|-
| 221900140
|-
| 221900159
|-
| 221900168
|-
| 221900175
|-
| 221900183
|-
| 221900187
|-
| 221900208
|-
| 221900209
|-
| 221900210
|-
| 221900216
|-
| 221900220
|-
| 221900223
|-
| 221900230
|-
| 221900234
|-
| 221900236
|-
| 221900246
|-
| 221900263
|-
| 221900264
|-
| 221900268
|-
| 221900270
|-
| 221900277
|-
| 221900309
|-
| 221900311
|-
| 221900318
|-
| 221900320
|-
| 221900323
|-
| 221900324
|-
| 221900325
|-
| 221900326
|-
| 221900328
|-
| 221900328
|-
| 221900339
|-
| 221900342
|-
| 221900346
|-
| 221900347
|-
| 221900353
|-
| 221900362
|-
| 221900371
|-
| 221900375
|-
| 221900379
|-
| 221900387
|-
| 221900406
|-
| 221900418
|-
| 221900425
|-
| 221900426
|-
| 221900431
|-
| 221900431
|-
| 221900450
|-
| 221900455
|-
| 221900461
|-
| 221900477
|-
| 221900490
|-
| 221900497
|-
| 231170041
|-
| 231830131
|-
| 231880007
|-
| 231880027
|-
| 231880035
|-
| 231880038
|-
| 231880042
|-
| 231880072
|-
| 231880076
|-
| 231880078
|-
| 231880087
|-
| 231880092
|-
| 231880098
|-
| 231880099
|-
| 231880102
|-
| 231880114
|-
| 231880135
|-
| 231880166
|-
| 231880167
|-
| 231880184
|-
| 231880185
|-
| 231880199
|-
| 231880199
|-
| 231880224
|-
| 231880227
|-
| 231880245
|-
| 231880247
|-
| 231880255
|-
| 231880266
|-
| 231880267
|-
| 231880270
|-
| 231880275
|-
| 231880276
|-
| 231880280
|-
| 231880292
|-
| 231880292
|-
| 231880313
|-
| 232188031
|-
| 231880316
|-
| 231880324
|-
| 231880340
|-
| 231880350
|-
| 231880357
|-
| 231880367
|-
| 231880382
|-
| 231880395
|-
| 231880403
|-
| 231880410
|-
| 231880423
|-
| 231880426
|-
| 231880429
|-
| 231880433
|-
| 231880439
|-
| 231880443
|-
| 231880472
|-
| 231880474
|-
| 231880481
|-
| 231880498
|-
| 231880513
|-
| 231880514
|-
| 231880515
|-
| 231880523
|}
</center>

数据科学基础 (Fall 2024)/第一次作业提交名单

2024-10-15T11:17:33Z

Zhoucan:

<center>
{| class="wikitable"
|-
! 学号
|-
| 221200004
|-
| 221850088
|-
| 221850088
|-
| 221850088
|-
| 221870109
|-
| 221900009
|-
| 221900024
|-
| 221900028
|-
| 221900029
|-
| 221900036
|-
| 221900038
|-
| 221900042
|-
| 221900046
|-
| 221900055
|-
| 221900068
|-
| 221900073
|-
| 221900075
|-
| 221900076
|-
| 221900083
|-
| 221900084
|-
| 221900085
|-
| 221900091
|-
| 221900091
|-
| 221900124
|-
| 221900128
|-
| 221900140
|-
| 221900159
|-
| 221900168
|-
| 221900175
|-
| 221900183
|-
| 221900187
|-
| 221900208
|-
| 221900209
|-
| 221900210
|-
| 221900216
|-
| 221900220
|-
| 221900223
|-
| 221900230
|-
| 221900234
|-
| 221900236
|-
| 221900246
|-
| 221900263
|-
| 221900264
|-
| 221900268
|-
| 221900270
|-
| 221900277
|-
| 221900309
|-
| 221900311
|-
| 221900318
|-
| 221900320
|-
| 221900323
|-
| 221900324
|-
| 221900325
|-
| 221900326
|-
| 221900328
|-
| 221900328
|-
| 221900339
|-
| 221900342
|-
| 221900346
|-
| 221900347
|-
| 221900353
|-
| 221900362
|-
| 221900371
|-
| 221900375
|-
| 221900379
|-
| 221900387
|-
| 221900406
|-
| 221900418
|-
| 221900425
|-
| 221900426
|-
| 221900431
|-
| 221900431
|-
| 221900450
|-
| 221900455
|-
| 221900461
|-
| 221900477
|-
| 221900490
|-
| 221900497
|-
| 231170041
|-
| 231830131
|-
| 231880007
|-
| 231880027
|-
| 231880035
|-
| 231880038
|-
| 231880042
|-
| 231880072
|-
| 231880076
|-
| 231880078
|-
| 231880087
|-
| 231880092
|-
| 231880098
|-
| 231880099
|-
| 231880102
|-
| 231880114
|-
| 231880135
|-
| 231880166
|-
| 231880167
|-
| 231880184
|-
| 231880185
|-
| 231880199
|-
| 231880199
|-
| 231880224
|-
| 231880227
|-
| 231880245
|-
| 231880247
|-
| 231880255
|-
| 231880266
|-
| 231880267
|-
| 231880270
|-
| 231880275
|-
| 231880276
|-
| 231880280
|-
| 231880292
|-
| 231880292
|-
| 231880313
|-
| 231880316
|-
| 231880324
|-
| 231880340
|-
| 231880350
|-
| 231880357
|-
| 231880367
|-
| 231880382
|-
| 231880395
|-
| 231880403
|-
| 231880410
|-
| 231880423
|-
| 231880426
|-
| 231880429
|-
| 231880433
|-
| 231880439
|-
| 231880443
|-
| 231880472
|-
| 231880474
|-
| 231880481
|-
| 231880498
|-
| 231880513
|-
| 231880514
|-
| 231880515
|-
| 231880523
|-
| 232188031
|}
</center>

数据科学基础 (Fall 2024)/第一次作业提交名单

2024-10-15T03:25:25Z

Zhoucan:

<center>
{| class="wikitable"
|-
! 学号
|-
| 221200004
|-
| 221850088
|-
| 221850088
|-
| 221850088
|-
| 221870109
|-
| 221900009
|-
| 221900024
|-
| 221900028
|-
| 221900029
|-
| 221900036
|-
| 221900038
|-
| 221900042
|-
| 221900046
|-
| 221900055
|-
| 221900068
|-
| 221900073
|-
| 221900075
|-
| 221900076
|-
| 221900083
|-
| 221900084
|-
| 221900085
|-
| 221900091
|-
| 221900091
|-
| 221900124
|-
| 221900128
|-
| 221900140
|-
| 221900159
|-
| 221900168
|-
| 221900175
|-
| 221900183
|-
| 221900187
|-
| 221900208
|-
| 221900209
|-
| 221900210
|-
| 221900216
|-
| 221900220
|-
| 221900223
|-
| 221900230
|-
| 221900234
|-
| 221900236
|-
| 221900246
|-
| 221900263
|-
| 221900264
|-
| 221900268
|-
| 221900270
|-
| 221900277
|-
| 221900309
|-
| 221900311
|-
| 221900318
|-
| 221900320
|-
| 221900323
|-
| 221900324
|-
| 221900325
|-
| 221900326
|-
| 221900328
|-
| 221900328
|-
| 221900339
|-
| 221900342
|-
| 221900346
|-
| 221900347
|-
| 221900353
|-
| 221900362
|-
| 221900371
|-
| 221900375
|-
| 221900379
|-
| 221900406
|-
| 221900418
|-
| 221900425
|-
| 221900426
|-
| 221900431
|-
| 221900431
|-
| 221900450
|-
| 221900455
|-
| 221900461
|-
| 221900477
|-
| 221900490
|-
| 221900497
|-
| 231170041
|-
| 231830131
|-
| 231880007
|-
| 231880027
|-
| 231880035
|-
| 231880038
|-
| 231880042
|-
| 231880072
|-
| 231880076
|-
| 231880078
|-
| 231880087
|-
| 231880092
|-
| 231880098
|-
| 231880099
|-
| 231880102
|-
| 231880114
|-
| 231880135
|-
| 231880166
|-
| 231880167
|-
| 231880184
|-
| 231880185
|-
| 231880199
|-
| 231880199
|-
| 231880224
|-
| 231880227
|-
| 231880245
|-
| 231880247
|-
| 231880255
|-
| 231880266
|-
| 231880267
|-
| 231880270
|-
| 231880275
|-
| 231880276
|-
| 231880280
|-
| 231880292
|-
| 231880292
|-
| 231880313
|-
| 231880316
|-
| 231880324
|-
| 231880340
|-
| 231880350
|-
| 231880357
|-
| 231880367
|-
| 231880382
|-
| 231880395
|-
| 231880403
|-
| 231880410
|-
| 231880423
|-
| 231880426
|-
| 231880429
|-
| 231880433
|-
| 231880439
|-
| 231880443
|-
| 231880472
|-
| 231880474
|-
| 231880481
|-
| 231880498
|-
| 231880513
|-
| 231880514
|-
| 231880515
|-
| 231880523
|-
| 232188031
|}
</center>

数据科学基础 (Fall 2024)/第一次作业提交名单

2024-10-15T02:51:07Z

Zhoucan:

<center>
{| class="wikitable"
|-
! 学号
|-
| 221200004
|-
| 221850088
|-
| 221850088
|-
| 221850088
|-
| 221870109
|-
| 221900009
|-
| 221900024
|-
| 221900028
|-
| 221900029
|-
| 221900036
|-
| 221900038
|-
| 221900042
|-
| 221900046
|-
| 221900055
|-
| 221900068
|-
| 221900073
|-
| 221900075
|-
| 221900076
|-
| 221900083
|-
| 221900084
|-
| 221900085
|-
| 221900091
|-
| 221900091
|-
| 221900124
|-
| 221900128
|-
| 221900140
|-
| 221900159
|-
| 221900168
|-
| 221900175
|-
| 221900183
|-
| 221900187
|-
| 221900208
|-
| 221900209
|-
| 221900210
|-
| 221900216
|-
| 221900220
|-
| 221900223
|-
| 221900230
|-
| 221900234
|-
| 221900236
|-
| 221900246
|-
| 221900263
|-
| 221900264
|-
| 221900268
|-
| 221900270
|-
| 221900277
|-
| 221900309
|-
| 221900311
|-
| 221900318
|-
| 221900320
|-
| 221900323
|-
| 221900324
|-
| 221900325
|-
| 221900326
|-
| 221900328
|-
| 221900328
|-
| 221900339
|-
| 221900342
|-
| 221900347
|-
| 221900353
|-
| 221900362
|-
| 221900371
|-
| 221900375
|-
| 221900379
|-
| 221900406
|-
| 221900418
|-
| 221900425
|-
| 221900426
|-
| 221900431
|-
| 221900431
|-
| 221900450
|-
| 221900455
|-
| 221900461
|-
| 221900477
|-
| 221900490
|-
| 221900497
|-
| 231170041
|-
| 231830131
|-
| 231880007
|-
| 231880027
|-
| 231880035
|-
| 231880038
|-
| 231880042
|-
| 231880072
|-
| 231880076
|-
| 231880078
|-
| 231880087
|-
| 231880092
|-
| 231880098
|-
| 231880099
|-
| 231880102
|-
| 231880114
|-
| 231880135
|-
| 231880166
|-
| 231880167
|-
| 231880184
|-
| 231880185
|-
| 231880199
|-
| 231880199
|-
| 231880224
|-
| 231880227
|-
| 231880245
|-
| 231880247
|-
| 231880255
|-
| 231880266
|-
| 231880267
|-
| 231880270
|-
| 231880275
|-
| 231880276
|-
| 231880280
|-
| 231880292
|-
| 231880292
|-
| 231880313
|-
| 231880316
|-
| 231880324
|-
| 231880340
|-
| 231880350
|-
| 231880357
|-
| 231880367
|-
| 231880382
|-
| 231880395
|-
| 231880403
|-
| 231880410
|-
| 231880423
|-
| 231880426
|-
| 231880429
|-
| 231880433
|-
| 231880439
|-
| 231880443
|-
| 231880472
|-
| 231880474
|-
| 231880481
|-
| 231880498
|-
| 231880513
|-
| 231880514
|-
| 231880515
|-
| 231880523
|-
| 232188031
|}
</center>

数据科学基础 (Fall 2024)/第一次作业提交名单

2024-10-15T02:39:04Z

Zhoucan:

<center>
{| class="wikitable"
|-
! 学号
|-
| 221200004
|-
| 221850088
|-
| 221850088
|-
| 221850088
|-
| 221870109
|-
| 221900009
|-
| 221900024
|-
| 221900028
|-
| 221900029
|-
| 221900036
|-
| 221900038
|-
| 221900042
|-
| 221900046
|-
| 221900055
|-
| 221900068
|-
| 221900073
|-
| 221900075
|-
| 221900076
|-
| 221900083
|-
| 221900084
|-
| 221900085
|-
| 221900091
|-
| 221900091
|-
| 221900124
|-
| 221900128
|-
| 221900140
|-
| 221900159
|-
| 221900168
|-
| 221900175
|-
| 221900183
|-
| 221900187
|-
| 221900208
|-
| 221900209
|-
| 221900210
|-
| 221900216
|-
| 221900220
|-
| 221900223
|-
| 221900230
|-
| 221900234
|-
| 221900236
|-
| 221900246
|-
| 221900263
|-
| 221900264
|-
| 221900268
|-
| 221900270
|-
| 221900277
|-
| 221900309
|-
| 221900311
|-
| 221900320
|-
| 221900323
|-
| 221900324
|-
| 221900325
|-
| 221900326
|-
| 221900328
|-
| 221900328
|-
| 221900339
|-
| 221900347
|-
| 221900353
|-
| 221900362
|-
| 221900371
|-
| 221900375
|-
| 221900379
|-
| 221900406
|-
| 221900418
|-
| 221900425
|-
| 221900426
|-
| 221900431
|-
| 221900431
|-
| 221900450
|-
| 221900455
|-
| 221900461
|-
| 221900477
|-
| 221900490
|-
| 221900497
|-
| 231170041
|-
| 231830131
|-
| 231880007
|-
| 231880027
|-
| 231880035
|-
| 231880038
|-
| 231880042
|-
| 231880072
|-
| 231880076
|-
| 231880078
|-
| 231880087
|-
| 231880092
|-
| 231880098
|-
| 231880099
|-
| 231880102
|-
| 231880114
|-
| 231880135
|-
| 231880166
|-
| 231880167
|-
| 231880184
|-
| 231880185
|-
| 231880199
|-
| 231880199
|-
| 231880224
|-
| 231880227
|-
| 231880245
|-
| 231880247
|-
| 231880255
|-
| 231880266
|-
| 231880267
|-
| 231880270
|-
| 231880275
|-
| 231880276
|-
| 231880280
|-
| 231880292
|-
| 231880292
|-
| 231880313
|-
| 231880316
|-
| 231880324
|-
| 231880340
|-
| 231880350
|-
| 231880357
|-
| 231880367
|-
| 231880382
|-
| 231880395
|-
| 231880403
|-
| 231880410
|-
| 231880423
|-
| 231880426
|-
| 231880429
|-
| 231880433
|-
| 231880439
|-
| 231880443
|-
| 231880472
|-
| 231880474
|-
| 231880481
|-
| 231880498
|-
| 231880514
|-
| 231880515
|-
| 231880523
|-
| 232188031
|}
</center>

数据科学基础 (Fall 2024)/第一次作业提交名单

2024-10-15T02:28:29Z

Zhoucan:

<center>
{| class="wikitable"
|-
! 学号
|-
| 221200004
|-
| 221850088
|-
| 221850088
|-
| 221850088
|-
| 221870109
|-
| 221900009
|-
| 221900024
|-
| 221900028
|-
| 221900029
|-
| 221900036
|-
| 221900042
|-
| 221900046
|-
| 221900055
|-
| 221900068
|-
| 221900073
|-
| 221900073
|-
| 221900075
|-
| 221900076
|-
| 221900083
|-
| 221900084
|-
| 221900085
|-
| 221900091
|-
| 221900091
|-
| 221900124
|-
| 221900128
|-
| 221900140
|-
| 221900159
|-
| 221900168
|-
| 221900175
|-
| 221900183
|-
| 221900187
|-
| 221900208
|-
| 221900209
|-
| 221900210
|-
| 221900216
|-
| 221900220
|-
| 221900223
|-
| 221900230
|-
| 221900234
|-
| 221900236
|-
| 221900246
|-
| 221900263
|-
| 221900264
|-
| 221900268
|-
| 221900270
|-
| 221900277
|-
| 221900309
|-
| 221900311
|-
| 221900320
|-
| 221900323
|-
| 221900324
|-
| 221900325
|-
| 221900326
|-
| 221900328
|-
| 221900328
|-
| 221900339
|-
| 221900347
|-
| 221900353
|-
| 221900362
|-
| 221900371
|-
| 221900375
|-
| 221900379
|-
| 221900406
|-
| 221900418
|-
| 221900425
|-
| 221900426
|-
| 221900431
|-
| 221900431
|-
| 221900450
|-
| 221900455
|-
| 221900461
|-
| 221900477
|-
| 221900490
|-
| 221900497
|-
| 231170041
|-
| 231830131
|-
| 231880007
|-
| 231880027
|-
| 231880035
|-
| 231880038
|-
| 231880042
|-
| 231880072
|-
| 231880076
|-
| 231880078
|-
| 231880087
|-
| 231880092
|-
| 231880098
|-
| 231880099
|-
| 231880102
|-
| 231880114
|-
| 231880135
|-
| 231880166
|-
| 231880167
|-
| 231880184
|-
| 231880185
|-
| 231880199
|-
| 231880199
|-
| 231880224
|-
| 231880227
|-
| 231880245
|-
| 231880247
|-
| 231880255
|-
| 231880266
|-
| 231880267
|-
| 231880270
|-
| 231880275
|-
| 231880276
|-
| 231880280
|-
| 231880292
|-
| 231880292
|-
| 231880313
|-
| 231880316
|-
| 231880324
|-
| 231880340
|-
| 231880350
|-
| 231880357
|-
| 231880367
|-
| 231880382
|-
| 231880395
|-
| 231880403
|-
| 231880410
|-
| 231880423
|-
| 231880426
|-
| 231880429
|-
| 231880433
|-
| 231880439
|-
| 231880443
|-
| 231880472
|-
| 231880474
|-
| 231880481
|-
| 231880498
|-
| 231880514
|-
| 231880515
|-
| 231880523
|-
| 232188031
|}
</center>