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# 400Hw06 - STAT 400 Spring 2011 Homework#6(due Friday March...

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STAT 400 Spring 2011 Homework #6 (due Friday, March 4, by 3:00 p.m.) From the textbook: 8th edition ( ) 1. 3.3-2 (a) , 3.3-4 (a) ( , ) 2. 3.3-2 (b) , 3.3-4 (b) ( , ) 3. 3.3-2 (c) , 3.3-4 (c) ( , ) 4. 3.3-8 ( ) 5. 3.3-24 (a),(b) ( ) 6. 3.4-4 ( ) 7. 3.4-8 ( ) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ NOT from the textbook: 8. 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 μ X = E ( X ) . e) Find σ X 2 = Var ( X ) .

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9. Let X be a continuous random variable with the probability density function f ( x ) = k x 2 , 0 x 1, f ( x ) = 0, otherwise. a) What must the value of k be so that f ( x ) is a probability density function? b) Find the probability P( 0.4 X 0.8 ). c) Find the median of the distribution of X. d) Find μ X = E ( X ). e) Find σ X = SD ( X ). f) Find the moment-generating function of X, M X ( t ) . 10. Suppose a random variable X has the following probability density function: = - otherwise 0 1 0 ) ( x C x f x e a) What must the value of C be so that f ( x ) is a probability density function?
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400Hw06 - STAT 400 Spring 2011 Homework#6(due Friday March...

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