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Lecture_2 Exercises

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

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Lecture 2 Exercises 1. Suppose the cdf of a continuous random variable X with support 0 1 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) P Y # . c) Find the cdf of Y. 3. The continuous random variable U has support (0, ) % with pdf given by 1 ( ) ( ) u u e f u " " & & # where 1 0 ( ) u u e du " " % & & # ( . a) Show that (1) 1 # . b) For n a positive integer greater than 1, show that ( ) ( 1)! n n # & c) Find the cdf of U if 2 " # . 4. Suppose S is a discrete random variable with support {0,1,2,3,... }. If the pf is
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