概率论 (Summer 2013)/Problem Set 4: Difference between revisions
Jump to navigation
Jump to search
imported>Zhangchihao (Created page with "== Problem 1 == == Problem 2 == == Problem 3 == == Problem 4 ==") |
imported>Zhangchihao |
||
| Line 1: | Line 1: | ||
== Problem 1 == | == Problem 1 == | ||
Let <math>X_1,X_2,\dots,X_n</math> be independent geometrically distributed random variables each having expectation 2 (each of the <math>X_i</math> is an independent experiment counting the number of tosses of an unbiased coin up to and including the first HEADS). Let <math>X=\sum_{i=1}^nX_i</math> and <math>\delta</math> be a positive real constant. Derive the best upper bound you can on <math>\Pr[X>(1+\delta)(2n)]</math>. | |||
== Problem 2 == | == Problem 2 == | ||
== Problem 3 == | == Problem 3 == | ||
== Problem 4 == | == Problem 4 == | ||
Revision as of 11:25, 25 July 2013
Problem 1
Let [math]\displaystyle{ X_1,X_2,\dots,X_n }[/math] be independent geometrically distributed random variables each having expectation 2 (each of the [math]\displaystyle{ X_i }[/math] is an independent experiment counting the number of tosses of an unbiased coin up to and including the first HEADS). Let [math]\displaystyle{ X=\sum_{i=1}^nX_i }[/math] and [math]\displaystyle{ \delta }[/math] be a positive real constant. Derive the best upper bound you can on [math]\displaystyle{ \Pr[X\gt (1+\delta)(2n)] }[/math].