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EE 322 Probabilistic Methods for Electrical Engineers Homework 6 Assigned: 03/09. 03/15 Problem 1. Let X be a random variable with PDF fX . Find the...

I only need to do problem 4 of the attached file.
EE 322 Probabilistic Methods for Electrical Engineers — Homework 6 Assigned: 03/09. Due: 03/15 Problem 1. Let X be a random variable with PDF f X . Find the PDF of the random variable | X | in the following three cases. (a) X is exponentially distributed with parameter λ . (b) X is uniformly distributed in the interval [ - 1 , 2]. (c) f X is a general PDF. Problem 2. Determine the distribution of Y = X 2 if X is Laplacian distributed: f X ( x ) = λ 2 e - λ | x | . Problem 3. Suppose you know how to generate using computer a random number X that is uniformly distributed on (0 , 1). How can you suitably transform the generated random variable to get an exponentially distributed random variable. That is, ±nd a function g ( X ) such that Y = g ( X ) is an exponential random variable with parameter λ . Problem 4. (30 points) Let X be a continuous random variable that it uniformly dis- tributed between 0 and 1. When X is given, Y is uniformly distributed between X and 2 X . (a) Find the variance of Y . (b) Find the correlation coe²cient between X and Y . (c) Use MATLAB to generate a plot of 1000 realizations of X and Y . Plot each realization as a point labeled ’+’ on the two-dimensional plane. You need to include both the MATLAB code and the plot. END OF ASSIGNMENT 1
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