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== Problem 1: Arbitrary Random Variables == | == Problem 1: Arbitrary Random Variables == | ||
| + | Let <math>F</math> be a non-decreasing function with | ||
| + | |||
| + | <math>lim_{x\rightarrow -\infty} F(x) = 0 | ||
| + | \mbox{ and } \lim_{x\rightarrow +\infty} F(x) = 1.</math> | ||
| + | |||
| + | Let $U$ be a uniform random variable on $[0,1]$. | ||
| + | \begin{enumerate} | ||
| + | \item Let $X = F^{-1}(U)$. What is the CDF of $X$? (Note $F^{-1}$ is the inverse of $F$. A function $g$ is the inverse of $F$ if $F(g(x)) = x$ for all $x$) | ||
| + | \item How can you generate an exponential random variable from $U$? | ||
== Problem 2: Gaussian Generation == | == Problem 2: Gaussian Generation == | ||
Revision as of 07:59, 15 October 2008
Contents
Instructions
Homework 7 can be downloaded here on the ECE 302 course website.
Problem 1: Arbitrary Random Variables
Let $ F $ be a non-decreasing function with
$ lim_{x\rightarrow -\infty} F(x) = 0 \mbox{ and } \lim_{x\rightarrow +\infty} F(x) = 1. $
Let $U$ be a uniform random variable on $[0,1]$. \begin{enumerate} \item Let $X = F^{-1}(U)$. What is the CDF of $X$? (Note $F^{-1}$ is the inverse of $F$. A function $g$ is the inverse of $F$ if $F(g(x)) = x$ for all $x$) \item How can you generate an exponential random variable from $U$?
