ECE-353-MIDTERM-II-W12.pdf

ECE-353-MIDTERM-II-W12.pdf - ECE 353 MIDTERM EXAM II Winter...

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ECE 353 MIDTERM EXAM II Winter 2012 Instructions : This is a closed-notes, closed-book exam. You are allowed to use an 8.5”x11” crib sheet and a basic calculator. You must justify your answers in order to receive full credit for your work. Answers without justification are awarded no credit whatsoever. 1. The random variable Y is related to the random variable T through the function 2 T Y e = , where T is the time between two occurrences of a Poisson process with parameter 1 2 λ = . a) (5 pts) What is the cumulative distribution function of Y, i.e., ( ) Y F y ? b) (5 pts) What is the probability density function of Y , i.e., ( ) Y f y ? c) (5 pts) What is the expected value of Y , i.e., { } E Y ? 2. The joint probability mass function of the random variables
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