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].
- (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
The most popular random number generator in the computer language C is drand48; a call
X = drand48()
results in X being a uniform random variable on [0,1]. How can you generate a gaussian random variable in C using drand48 ? (Hint: use 1(b) above, and problem 4 of HW 6)
