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].

• (a) 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 $)
• (b)How can you generate an exponential random variable from $ U $?

Problem 2: Gaussian Generation

Problem 3: A Random Parameter

Problem 4: Debate Date