assignment_5_08 - ESO 209 PROBABILITY STATISTICS Semester 2...

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ESO 209: PROBABILITY & STATISTICS Semester 2: 2007-08 Assignment #5 Instructor: Amit Mitra [1] Let be a Poisson random variable with parameter X λ . Find the probability mass function of . 2 5 Y X = [2] Let be Binomial random variable with parameters and X n p . Find the probability mass function of Y n X = . [3] Consider the discrete random variable with the probability mass function X ( ) ( ) ( ) ( ) ( ) ( ) 1 1 2 , 1 , 0 , 5 6 1 10 1 , 2 , 3 15 30 30 P X P X P X P X P X P X = − = = − = = = = = = = = = 1 5 1 . Find the probability mass function of 2 . Y X = [4] The probability mass function of the random variable is given by X ( ) 1 2 0,1,2,... 3 3 0 otherwi x x P X x = = = se. Find the distribution of ( ) 1 . Y X X = + [5] The probability density function of the random variable is X ( ) 1 0 1 0 otherwise. X x f x < < = i.e. ( ) ~ 0,1 X U . Find the distribution of the following functions of X (a) Y X = (b) 2 Y X = (c) 2 3 Y X = + (d) log ; 0. Y X λ λ = − > [6] Let be a random variable with X ( ) 0, , U θ 0 θ > distribution. Find the distribution of ( ) min , 2 . Y X θ =
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