Prob18W-06.pdf

# Prob18W-06.pdf - ELG 3126 RANDOM SIGNALS AND SYSTEMS Winter...

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ELG 3126 RANDOM SIGNALS AND SYSTEMS Winter 2018 ASSIGNMENT 6 (due at 11:30 AM Thursday, March 1 in class) 1. A student number at the University of Ottawa is a string of 7 digits in a row. A random experiment consists of picking at random a digit from one such student number—your student number. Suppose we then define a random variable X to correspond to the value of the chosen digit. Find the mean and variance of that random variable. 2. Find the mean and variance of the random variable X having the pdf given in Question 1 on the previous assignment. 3. If X U ( - 2 , 4), find the probability density function of the random variable Y = 2 X + 3. 4. If X U ( - 2 , 4), find the probability density function of the random variable Y = 1 / ( X + 2) 4 . 5. If X U ( - 2 , 4), find the probability density function of the random variable Y = X 2 u ( X ), where u ( x ) is the unit step function. Hint : First sketch g ( x ) = x 2 u ( x ). 6. Let X be a Gaussian random variable with mean 3 and variance 4. Find the pdf of the random variable Y = g ( X ) if g ( x ) = xu ( x ) + x 3 u ( - x ).
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