STAT 400 hw5 - STAT 400 Fall 2011 Homework #5 (10 points)...

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STAT 400 Fall 2011 Homework #5 (10 points) (due Friday, Feb 24th, by 3:00 p.m.) No credit will be given without supporting work. 1. Suppose a random variable X has the following probability density function: otherwise 0 1 1 ) ( C x x x f a) What must the value of C be so that f ( x ) is a probability density function? b) Find P ( X < 2 ). c) Find P ( X < 3 ). d) Find X = E ( X ). e) Find X 2 = Var ( X ). 2. Suppose a random variable X has the following probability density function: otherwise x 0 3 0 | ) ( x f | 2 - x C a) What must the value of C be so that f ( x ) is a probability density function? b) Find the cumulative distribution function F ( x ) = P ( X x ). c) Find the median of the probability distribution of X. d) Find X = E ( X ). e) Find the moment-generating function of X, M X ( t ).
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3. Let X be a continuous random variable with the probability density function f ( x ) = k x 2 , 0 x 1, f ( x ) = 0,
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STAT 400 hw5 - STAT 400 Fall 2011 Homework #5 (10 points)...

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