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Unformatted text preview: Stat 414 Homework 8 Fall 2008 1. 3.215 (5 points) ) ( ) 1 ( ) 1 ( ) 1 ( 1 1 1 ) 1 1 ( 1 ) 1 ( ) ( , ) 1 ( ) 1 ( ) 1 )( ( ) ( ' ) ( 2 2 2 2 2 2 2 2 2 2 2 a f e e e e e e e e e e e e e e e a f x e e e e e e x F x f a a a a a a a a a a a a a a a x x x x x x = + = + = + = + = + = + = + < < + = + = + = = Because f(a) = f(a) the graph of the pdf is symmetric about x = 0. 2. 3.2 22 (5 points) The cdf 4 4 4 4 1 ) ( 4 ) ( 4 3 t t x t x t x e e x d e dx e x t F = = = = P(X > 2) = 1  P(X 2) = 16 2 2 4 4 ) 1 ( 1 = = e e e (X is in thousands of gallons) 3. 3.3  6 ad (not e) (8 points) Since = 20, we have , 1 ) ( 20 > = x e x F x One important note is that if X is a continuous random variable P(X < x) = P(X x). This is not true under discrete cases....
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 Fall '07
 SENTURK,DAMLA

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