Unformatted text preview: + V X n = 9 n 4 Alternative Solution. Let Y = j be the number of 1bits in the string chosen. Then X = 3 Y and the random variable Y has the binomial distribution with the parameters p = q = 1 / 2 on the set { , 1 , . . . , n } . Therefore, by the results of Example 5 and Example 18 in Ch 6.4 we have EX = np = n/ 2 and V X = npq = n/ 4. Since X = 3 Y , we have EX = 3 EY = 3 n/ 2 and V X = 3 2 V Y = 9 n/ 4. 1...
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This note was uploaded on 01/27/2010 for the course MATH 213 taught by Professor Jack during the Spring '08 term at University of Illinois at Urbana–Champaign.
 Spring '08
 JACK
 Math

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