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# assign04 - Math 302.102 Fall 2010 Assignment #4 This...

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Assignment #4 This assignment is due at the beginning of class on Friday, October 15, 2010. 1. In each of the following cases, compute P { 0 < X < 2 } where the random variable X has the given probability density function. (a) f ( x ) = ( x - 2 , x 1 , 0 , x < 1 . (b) f ( x ) = ( 7 e - 7 x , x 0 , 0 , x < 0 . (c) f ( x ) = e e 2 - 5 x 2 e - x , - 1 x 1 , 0 , otherwise . (d) f ( x ) = ( xe - x , x 0 , 0 , x < 0 . 2. Suppose that the random variable X has density function f ( x ) = ( 1 8 x 0 x 4 , 0 , otherwise . (a) Determine the value of a such that P { X a } = 1 2 . (b) Determine the value of a such that P { X a } = 1 4 . 3. Suppose that the random variable X has distribution function F ( x ) = 0 , x < 0 , 1 8 x 3 , 0 x 2 , 1 x > 2 . (a) Compute P { X 1 } . (b) Compute P { 0 . 5 X 1 . 5 } . (c) Determine the value of a such that P { X a } = 1 2 . (d)

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## This note was uploaded on 04/07/2011 for the course MATH 302 taught by Professor Israel during the Spring '08 term at UBC.

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assign04 - Math 302.102 Fall 2010 Assignment #4 This...

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