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Consider the following game: A player throws a fair die repeatedly until he rolls a 2

ISBN: 9780495110811 47

Solution for problem 3.187 Chapter 3

Mathematical Statistics with Applications | 7th Edition

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Problem 3.187

Consider the following game: A player throws a fair die repeatedly until he rolls a 2, 3, 4, 5, or 6. In other words, the player continues to throw the die as long as he rolls 1s. When he rolls a non-1, he stops. a What is the probability that the player tosses the die exactly three times? b What is the expected number of rolls needed to obtain the first non-1? c If he rolls a non-1 on the first throw, the player is paid \$1. Otherwise, the payoff is doubled for each 1 that the player rolls before rolling a non-1. Thus, the player is paid \$2 if he rolls a 1 followed by a non-1; \$4 if he rolls two 1s followed by a non-1; \$8 if he rolls three 1s followed by a non-1; etc. In general, if we let Y be the number of throws needed to obtain the first non-1, then the player rolls (Y 1) 1s before rolling his first non-1, and he is paid 2Y1 dollars. What is the expected amount paid to the player?

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Chapter 5 Bivariate Data­ two variables for on individual to find a relationship between one another When analyzing describe each variable and describe the relationship Explanatory variable­ X, used to predict, independent Response variable­ Y, dependent Scatterplot­ the variables measured by the same individual Linear relationship­ straight line Non­linear relationship­ a relationship...

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