Homework_6

Homework_6 - ECE600 Random Variables and Waveforms Spring...

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ECE600 Random Variables and Waveforms Mark R. Bell Spring 20 1 1 MSEE 336 Homework Assignment #6 Should be completed by Session 17 Reading Assignment: Read Sections 5-4, 5-5, and 6-1 through 6-3 of Papoulis. Note: Problem numbers from Papoulis refer to fourth edition, with equivalent third edition problens give in parentheses. 1. Papoulis 5-22 (5-18 in 3rd edition). 2. Papoulis 5-23 (5-19 in 3rd edition). 3. Papoulis 5-33 (5-21 in 3rd edition). 4. Papoulis 5-27 (5-23 in 3rd edition). 5. Let X be a binomially distributed random variable with P ( { X = k } )= ± n k ² p k (1 p ) n k ,k =0 , 1 ....,n . Find the mean and variance of X . 6. A Gamma distributed random variable X has pdf f X ( x β α Γ( α ) x α 1 e βx 1 (0 , ) ( x ) , where Γ( a ³ 0 u a 1 e u du, where α> 0 and β> 0. Calculate the mean and variance of
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