If the player is paid 3y dollars what is the expected

Reference no: EM13643602

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 1's. Let Y be the number of throws needed to obtain the first non-one.

a) If X ? geo(p), then show that E[X] = 1/p

b) What is the probability that the player tosses the die more than two times given that the player tosses it more than once? Explain why this property is called the memoryless property.

c) If the player is paid 3Y dollars, what is the expected amount paid to the player?

d) What is the probability that the player tosses the die at least four times to obtain the two non-1's?

Reference no: EM13643602

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