assignment_5_08

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 YX =− [2] Let be Binomial random variable with parameters and X n p . Find the probability mass function of YnX = . [3] Consider the discrete random variable with the probability mass function X () 11 2, 1, 0, 56 0 2 , 3 15 30 30 PX = = = = == = = 1 5 1 . Find the probability mass function of 2 . = [4] The probability mass function of the random variable is given by X 12 0,1,2,. .. 33 0o t h e r w i x x PX x ⎛⎞ = ⎜⎟ ⎝⎠ s e . Find the distribution of ( ) 1. YXX =+ [5] The probability density function of the random variable is X 10 1 0 otherwise. X x fx << = i.e. ( ) ~0 , 1 XU . Find the distribution of the following functions of X (a) = (b) 2 = (c) 23 (d) log ; 0. > [6] Let be a random variable with X ( ) 0, , U θ 0 > distribution. Find the distribution of min , 2 . =
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[7] The probability density function of is given by X () 1 12 32 2 0o t h e r w i s e . X x fx −≤ = Find the distribution of . 2 YX = [8] The probability density function of is given by X 1 0 1 t h e p pq X x kx x + > = + r w i s e , 0 , p q > . Derive the distribution of
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This note was uploaded on 08/19/2009 for the course EE EE210 taught by Professor J.john during the Spring '08 term at IIT Kanpur.

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assignment_5_08 - ESO 209 PROBABILITY STATISTICS Semester 2...

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