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# Hw02 - STAT 410 Spring 2008 Homework#2(due Friday February...

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Unformatted text preview: STAT 410 Spring 2008 Homework #2 (due Friday, February 1, by 3:00 p.m.) 1. Below is a list of moment-generating functions. Provide the mean and variance of the random variable associated with each. ( Justify your answers. ) a) M X ( t ) = 10 5 3 5 2 & & ¡ ¢ £ £ ¤ ¥ + t e . b) M X ( t ) = 6 2 . 1 1 & ¡ ¢ £ ¤ ¥- t , t < 5. c) M X ( t ) = 6 2 . 1 8 . & & & & & ¡ ¢ £ £ £ £ £ ¤ ¥- t t e e , t < ln 5. d) M X ( t ) = e 5 t . 2. Let Y denote a random variable with probability density function given by f ( y ) = 2 1 y e- , – ∞ < y < ∞ . a) Find the moment-generating function of Y. ( Be sure to indicate its domain ! ) b) Find E ( Y ). c) Find Var ( Y ). 3. An insurance policy reimburses a loss up to a benefit limit of 10. The policyholder’s loss, Y, follows a distribution with density function: f ( y ) = ¦ ¦ § ¦ ¦ ¨ © > otherwise 1 if 2 3 y y What is the expected value of the benefit paid under the insurance policy? 4. The time, T, that a manufacturing system is out of operation has cumulative distribution...
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Hw02 - STAT 410 Spring 2008 Homework#2(due Friday February...

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