概率论与数理统计 (Spring 2023)/Problem Set 4: Difference between revisions
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:'''Input:''' real numbers <math>U < 1</math>; | :'''Input:''' real numbers <math>U < 1</math>; | ||
---- | ---- | ||
: | : | ||
:initialize <math>x = 1</math> and <math>count = 0</math>; | :initialize <math>x = 1</math> and <math>count = 0</math>; | ||
:while <math> x > U </math> do | :while <math> x > U </math> do | ||
Revision as of 08:47, 22 May 2023
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Assumption throughout Problem Set 4
Without further notice, we are working on probability space [math]\displaystyle{ (\Omega,\mathcal{F},\mathbf{Pr}) }[/math].
Without further notice, we assume that the expectation of random variables are well-defined.
The term [math]\displaystyle{ \log }[/math] used in this context refers to the natural logarithm.
Problem 1
Algorithm - Input: real numbers [math]\displaystyle{ U \lt 1 }[/math];
- initialize [math]\displaystyle{ x = 1 }[/math] and [math]\displaystyle{ count = 0 }[/math];
- while [math]\displaystyle{ x \gt U }[/math] do
- choose [math]\displaystyle{ y \in (0,1) }[/math] uniformly at random;
- update [math]\displaystyle{ x = x * y }[/math] and [math]\displaystyle{ count = count + 1 }[/math];
- return [math]\displaystyle{ count }[/math];