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plugin-hw4 - CS206 HW4 October 20, 2009 (* due date is...

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Unformatted text preview: CS206 HW4 October 20, 2009 (* due date is November 4, 2009) 1. A fair die is tossed twice. Let X = the sum of the faces, Y = the maximum of the two faces, and Z = | face 1- face 2 | . (a) Write down the value of X , Y , Z , and W = XZ for each outcome w S . (b) Find Range ( X ), Range ( Y ), Range ( Z ), and Range ( W ). (c) Describe the partitions A X and A Z induced by these random variables. (d) Find f X , f Y , f Z , and f W , the frequency functions. (e) Are the events A = { w S : X ( w ) = 7 } and B = { w S : Z ( w ) = 1 } independent? 2. (*) A fair coin is tossed four times. Consider the following random variables on S , the sample space: X = the number of Heads; Y = the length of the longest block of successive Tails (0 if NO Tails); Z = the number of the toss on which the last Tail occurred (0 if NO Tails); W = max( X, Y ); V = min( X, Z ). (a) List the elements of S . For each w S , write the value of each random variable. (b) Find the Range of each random variable. (c) Find the frequency function of each random variable and plot it....
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This note was uploaded on 03/24/2011 for the course CS 206 taught by Professor Fredman during the Spring '08 term at Rutgers.

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plugin-hw4 - CS206 HW4 October 20, 2009 (* due date is...

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