HW6_Spring11

HW6_Spring11 - ELEC210 Spring 2011 Homework 6 1. Let X and...

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Unformatted text preview: ELEC210 Spring 2011 Homework 6 1. Let X and Y have joint pdf: () (a) Find ( ). (b) Find . (c) Find using part b. (d) Find . 2. A message requires N time units to be transmitted, where N is a geometric ( ) random variable with pmf A single new message arrives during a time unit with probability , and no messages arrive with probability . Let K be the number of new messages that arrive during the transmission of a single message. (a) Find and using conditional expectation. (b) Find the pmf of . Hint: ( ) ( ) ∑ () . 3. The number X of goals the Bulldogs score against the Flames has a geometric distribution with mean 2; the number of goals Y that the Flames score against the Bulldogs is also geometrically distributed but with mean 4. (a) Find the pmf of . Assume X and Y are independent. (b) What is the probability that the Bulldogs beat the Flames? Tie the Flames? (c) Find . 4. Let X and Y be independent random variables that are uniformly distributed in the interval . Find the pdf of . 5. Let X, Y, Z have joint pdf: ( ) ( ) (a) Find k. (b) Find ( ) and ( ). (c) Find ( ) ( ) and ( ). (d) Find the mean vector and covariance matrix for ( ). ...
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This note was uploaded on 10/16/2011 for the course ELEC 308,315,10 taught by Professor Prof.shenghuisong during the Spring '11 term at CUHK.

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