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

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Math 3C Homework 6 Solutions Ilhwan Jo and Akemi Kashiwada 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 0 . 1 - 0 . 5 0 . 2 0 . 1 0 . 1 0 . 5 0 . 25 1 0 . 35 Solution EX = X x xP ( X = x ) = ( - 1)(0 . 1) + ( - 0 . 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) + ( - 0 . 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 - 0 . 2850 2 0 . 4823 , σ = p var( X ) = 0 . 4823 0 . 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 . 1

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(b) P ( X 8) = P ( X = 8) + P ( X = 9) + P ( X = 10) = 10 8 1 2 10 + 10 9 1 2 10 + 10 10 1 2 10 = 10 8 + 10 9 + 10 10 ¶¶ 1 2 10 = 10 · 9 2 + 10 + 1 1 2 10 = 56 2 10 . (c) P ( X 9) = 1 - P ( X = 10) = 1 - 10 10 1 2 10 = 1 - 1 2 10 .
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hw6 - Math 3C Homework 6 Solutions Ilhwan Jo and Akemi...

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