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Unformatted text preview: f Y ( v ) = 1 + v,-1 v , v, < v 1 , , otherwise . Find 1. P ( | Y | < 1 2 ) 2. P ( Y > | Y < 1 2 ) 3. E [ Y ] . Problem 4 : Let X,Y,Z be independent uniformly distributed random variables on [0 , 1] . Let W = max( X,Y,Z ) and R = min( X,Y,Z ) . Find the pdf of W , the pdf of R , and the joint pdf of ( W,R ) . Problem 5 : A signal s = 3 is transmitted from a satellite but is corrupted by noise, and the received signal is X = s + W . When the weather is good, which happens with probability 2 3 , W is normal with zero mean and variance 4 . When the weather is bad, W is normal with zero mean and variance 9 . In the absence of any weather information: 1. What is the PDF of X ? 2. Calculate the probability that X is between 2 and 4 ....
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- Spring '07