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Unformatted text preview: Homework 3 Solutions Problem Solutions : Yates and Goodman, 2.2.5 2.3.4 2.3.6 2.4.2 2.4.5 2.5.6 2.5.7 2.6.3 and 2.6.4 Problem 2.2.5 Solution Using B (for Bad) to denote a miss and G (for Good) to denote a successful free throw, the sample tree for the number of points scored in the 1 and 1 is B 1- p G p B 1- p G p • Y =0 • Y =1 • Y =2 From the tree, the PMF of Y is P Y ( y ) = 1- p y = 0 p (1- p ) y = 1 p 2 y = 2 otherwise (1) Problem 2.3.4 Solution (a) Let X be the number of times the frisbee is thrown until the dog catches it and runs away. Each throw of the frisbee can be viewed as a Bernoulli trial in which a success occurs if the dog catches the frisbee an runs away. Thus, the experiment ends on the first success and X has the geometric PMF P X ( x ) = (1- p ) x- 1 p x = 1 , 2 , . . . otherwise (1) (b) The child will throw the frisbee more than four times iff there are failures on the first 4 trials which has probability (1- p ) 4 . If p = 0 . 2, the probability of more than four...
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- Fall '08
- Probability theory, PMF pX