hw3-sol - AMS 311 (Fall, 2011) Joe Mitchell PROBABILITY...

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Unformatted text preview: AMS 311 (Fall, 2011) Joe Mitchell PROBABILITY THEORY Homework Set # 3 Solution Notes (1). (30 points) Six women and five men apply for a job at Google. Three of the applicants are selected for interviews. Let X denote the number of women in the interview pool. (a). Give (explicitly) the probability mass function for X . Also show a plot of it. The possible values for X are { , 1 , 2 , 3 } . The probability mass function is given by p ( x ) = P ( X = x ) = ( 6 )( 5 3 ) ( 11 3 ) if x = 0 ( 6 1 )( 5 2 ) ( 11 3 ) if x = 1 ( 6 2 )( 5 1 ) ( 11 3 ) if x = 2 ( 6 3 )( 5 ) ( 11 3 ) if x = 3 otherwise The plot of p ( x ) has isolated dots of the appropriate heights at x = 0 , 1 , 2 , 3, with p ( x ) = 0 everywhere else. (b). Give (explicitly) the cdf, F ( x ) , for X . Also show a plot of it. The cdf is a staircase with step heights given by the spike heights of the pmf: F ( x ) = P ( X x ) = if x < ( 6 )( 5 3 ) ( 11 3 ) if 0 x < 1 ( 6 )( 5 3 ) ( 11 3 ) + ( 6 1 )( 5 2 ) ( 11 3 ) if 1 x < 2 ( 6 )( 5 3 ) ( 11 3 ) + ( 6 1 )( 5 2 ) ( 11 3 ) + ( 6 2 )( 5 1 ) ( 11 3 ) if 2 x < 3 1 if x 3 (c). What is the probability that more women are interviewed than men?...
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This note was uploaded on 10/20/2011 for the course AMS 311 taught by Professor Tucker,a during the Fall '08 term at SUNY Stony Brook.

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hw3-sol - AMS 311 (Fall, 2011) Joe Mitchell PROBABILITY...

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