Lecture_2 Exercises

# Lecture_2 Exercises - Lecture 2 Exercises 1. Suppose the...

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Lecture 2 Exercises 1. Suppose the cdf of a continuous random variable X with support 01 x !! is ( ) F x x " # a) What are the possible values for the parameter ? b) Find the median m of X defined by ( ) 1/ 2 P X m \$ # . c) Find the pdf of X. 2. Suppose that ( ) , 1,2,. ..,10 f y cy y ## is the probability function of a discrete random variable Y . a) Find the constant c . b) Find ( 5) PY # . c) Find the cdf of Y. 3. The continuous random variable U has support (0, ) % with pdf given by 1 () u ue fu && # where 1 0 u u e du % ’# ( . a) Show that (1) 1 . b) For n a positive integer greater than 1, show that ( ) ( 1)! nn #& c) Find the cdf of U if 2 # . 4. Suppose S is a discrete random variable with support {0,1,2,3,.
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## This note was uploaded on 10/21/2010 for the course MATHEMATIC stats taught by Professor Various during the Spring '10 term at Waterloo.

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