hw6 - Math 3C Homework 6 Solutions Ilhwan Jo and Akemi...

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Unformatted text preview: Math 3C Homework 6 Solutions Ilhwan Jo and Akemi Kashiwada ilhwanjo@math.ucla.edu, akashiwada@ucla.edu Assignment: Section 12.4 Problems 18, 29, 31, 32, 33, 34, 36, 38, 40 18. Suppose that the probability mass functions of a discrete random variable X is given by the following table. Find the mean, the variance, and the standard deviation of X . x P ( X = x )- 1 . 1- . 5 . 2 . 1 . 1 . 5 . 25 1 . 35 Solution EX = X x xP ( X = x ) = (- 1)(0 . 1) + (- . 5)(0 . 2) + (0 . 1)(0 . 1) + (0 . 5)(0 . 25) + (1)(0 . 35) = 0 . 2850 , EX 2 = X x x 2 P ( X = x ) = (- 1) 2 (0 . 1) + (- . 5) 2 (0 . 2) + (0 . 1) 2 (0 . 1) + (0 . 5) 2 (0 . 25) + (1) 2 (0 . 35) = 0 . 5635 , var( X ) = EX 2- ( EX ) 2 = 0 . 5635- . 2850 2 . 4823 , = p var( X ) = . 4823 . 6945 . 29. Toss a fair coin ten times. Let X be the number of heads. (a) Find P ( X = 5). (b) Find P ( X 8). (c) Find P ( X 9). Solution (a) X is binomially distributed with probability p = 1 2 of having a head. The number of trials is n = 10. P ( X = 5) = 10 5 1 2 5 1 2 5 = 10 5 1 2 10 ....
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This note was uploaded on 04/03/2008 for the course MATH 3C taught by Professor Schonmann during the Spring '07 term at UCLA.

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hw6 - Math 3C Homework 6 Solutions Ilhwan Jo and Akemi...

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