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# hw06 - STAT 225 Homework 6 Due Monday October 18 1 This...

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STAT 225 - Homework 6 Due Monday October 18 1. This homework is due Monday, October 18 in class, BEFORE class starts. 2. Please remember staple if you turn in more than one page. 3. You must always show all work. If you do not show your work, you may not receive full credit. Do the following problems. 1. Let the random variable X have the following pdf: f X ( x ) = kx (1 - x ) 2 0 < x < 1 0 otherwise (a) Determine the value of k so that f X ( x ) is a legitimate pdf. (b) Find P ( X > . 5). (c) Find E ( X ). 2. Suppose the failure time (in hundreds of hours) of a lightbulb is a random variable X with the following cumulative distribution function: F X ( x ) = 0 x < 0 1 - e - x 2 x 0 (a) Find f X ( x ). (b) Find the probability that the lightbulb lasts for at least 200 hours. (c) Find P ( X > 1 | X 2) 3. Let X have the density function given by: f X ( x ) = x 2 9 0 x c 0 otherwise (a) Find c so that f X ( x ) is a legitimate density function.

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