prob1-01-12-09-p1

prob1-01-12-09-p1 - MATH 11300 Probability AUTUMN 2009...

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Unformatted text preview: MATH 11300 Probability AUTUMN 2009 Problem Sheet 9 Questions marked * are to be handed in. *1. Let X be a continuous random variable taking values in the interval [- 3 , 3], with probability density function (pdf) f X given by f X ( x ) = (9- x 2 ) / 36- 3 ≤ x ≤ 3 otherwise . (a) Find the distribution function F X for X . (b) Find P ( X < 0) , P (- 2 ≤ X ≤ 1) and P ( X > 2 . 5). 2. Let X be a continuous random variable with distribution function F X given by F X ( x ) = 1- (1 + x ) e- x x > otherwise . Find the density function f X for X . Hence find E ( X ) and Var( X ) *3. Let Y be a continuous random variable taking values in the interval [0 , 1]. Assume Y has probability density function (pdf) proportional to y (1- y ), i.e. there exists a fixed constant c such that the pdf f Y is given by f Y ( y ) = cy (1- y ) 0 ≤ y ≤ 1 otherwise. (a) Find the value c must take for this to be a pdf....
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prob1-01-12-09-p1 - MATH 11300 Probability AUTUMN 2009...

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