Homework7 ECE302Fall2008sanghavi - Rhea

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 $U$?

Problem 2: Gaussian Generation

Problem 3: A Random Parameter

Problem 4: Debate Date