概率论与数理统计 (Spring 2023)/Problem Set 4: Difference between revisions

Revision as of 08:34, 22 May 2023

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.

Algorithm

{{{2}}}

@@ Line 11: / Line 11: @@
 <p>The term <math>\log</math> used in this context refers to the natural logarithm.</p>
+== Problem 1 ==
+{{Theorem|''Algorithm''|
+:'''Input:'''  real numbers <math>U < 1</math>;
+----
+:initialize <math>x = 1</math> and <math>count = 0</math>;
+:while <math> x > U </math> do
+:* choose <math>y \in (0,1)</math> uniformly at random;
+:* update </math>x = x * y</math> and <math>count = count + 1</math>;
+:return <math>C=E</math> (the parallel edges between the only two vertices in <math>V</math>);
+}}