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(2) A game consists of drawing tickets with numbers on them from a box, independ

ID: 3058891 • Letter: #

Question

(2) A game consists of drawing tickets with numbers on them from a box, independently with replacement. In order to play you have to stake $2 each time you draw a ticket. Your net gain is the number on the ticket you draw. Suppose there are 4 tickets in the box with numbers -2, -1, 0, 3 on them. If, for example the ticket shows $3 then you get your stake back, plus an additional $3. (a) Let I be the indicator of making a positive net gain on an single game. Find the mearn and variance of I. Hint: I is really a binomial random variable with n = 1, what is p? (b) Suppose that you play this game 300 times, and let S denote the number of times that you have a positive net gain. Give the mean and the variance of S. (c) Find an estimate of the probability that S is greater than equal to 90.

Explanation / Answer

(2) A game consists of drawing tickets with numbers on them from a box, independently with replacement. In order to play you have to stake $2 each time you draw a ticket. Your net gain is the number on the ticket you draw. Suppose there are 4 tickets in the box with numbers -2, -1, 0, 3 on them. If, for example the ticket shows $3 then you get your stake back, plus an additional $3. (a) Let I be the indicator of making a positive net gain on an single game. Find the mearn and variance of I. Hint: I is really a binomial random variable with n = 1, what is p? (b) Suppose that you play this game 300 times, and let S denote the number of times that you have a positive net gain. Give the mean and the variance of S. (c) Find an estimate of the probability that S is greater than equal to 90.