PracticeMidterm2 Solutions

# PracticeMidterm2 Solutions - Practice Midterm 2 1 1....

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Practice Midterm 2 1

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1. Suppose that the probability mass function of a discrete random variable X is given by the following table x P ( X = x ) -3 0.2 -1 0.3 1.5 0.4 2 0.1 Find and graph the corresponding distribution function F ( x ). Solution: F ( x ) = 0 x < - 3 0 . 2 - 3 x < - 1 0 . 5 - 1 x < 1 . 5 0 . 9 1 . 5 x < 2 1 x 2 2
2. Let X be a random variable with distribution function F ( x ) = 0 x < - 2 0 . 2 - 2 x < 0 0 . 3 0 x < 1 0 . 7 1 x < 2 1 x 2 Determine the probability mass function of X . Solution: x P ( X = x ) -2 0.2 0 0.1 1 0.4 2 0.3 3

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3. Suppose that the probability mass function of a discrete random variable X is given by the following table. x P ( X = x ) -2 0.1 -1 0.4 0 0.3 1 0.2 (a) Find EX . (b) Find EX 2 . (c) Find E [ X ( X - 1)]. (d) Find var ( X ). Solution: (a) EX = X x x · p ( x ) = ( - 2)(0 . 1) + ( - 1)(0 . 4) + (0)(0 . 3) + (1)(0 . 2) = - 0 . 4 (b) EX 2 = X x x 2 · p ( x ) = ( -
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## This note was uploaded on 07/14/2008 for the course MATH 3C taught by Professor Schonmann during the Winter '07 term at UCLA.

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PracticeMidterm2 Solutions - Practice Midterm 2 1 1....

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