Homework_8_Solution

# Homework_8_Solution - Stat 414 Homework 8 Fall 2008 1...

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Unformatted text preview: Stat 414 Homework 8 Fall 2008 1. 3.2-15 (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 a-d (not e) (8 points) Since θ = 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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Homework_8_Solution - Stat 414 Homework 8 Fall 2008 1...

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