hw8sol - Homework 8 Solutions Chapter 3: - x 68. Length of...

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Homework 8 Solutions Chapter 3: 68. Length of time to complete a job of a server has exponential pdfand cdf F X x = 1 e − x Call Y the waiting time until service of the first job. Its distribution is distribution of the 1 st order statistics. f Y y = f 1 y = nf X y  1 F X y  n 1 = n e − y 1 − 1 e − y  n 1 = n e − y e − y n 1 = n e n y , y 0 Call Z the waiting time until service of the second job. Its distribution is distribution of the 2 nd order statistics. f Z z = f 2 z = n n 1 f X z  F X z  2 1 1 F X z  n 2 = n n 1  e − z 1 e − z  1 − 1 e − z  n 2 = = n n 1  e − n 1  z 1 e − z = , y 0 Chapter 4: 6.Let X continuous random variable with pdf f X x = 2x , 0 x 1 a. Find
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