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 $U$?
