# hw10 - ORIE 3500/5500 Engineering Probability and...

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ORIE 3500/5500 – Engineering Probability and Statistics II Fall 2010 Assignment 10 Problem 1 As punishment for committing a particularly heinous crime you have been sentenced to jail under the following terms. Upon entering jail you draw a ball from a box containing balls numbered 0, 1 and 3 respectively. If you draw the ball numbered 0, you get out of jail immediately. If you draw 1 or 3, you replace the ball in the box and stay that many years in jail, at which time you draw again, under the same conditions. This is repeated until you draw the zero and go free. How long do you expect to be in jail? Hint : condition on the ﬁrst ball drawn. Problem 2 A lottery player decides to use a random variable gen- erator to help him decide how many tickets to buy. He generates a discrete uniform random variable N taking values of 1 through 5 with equal probabilities, and then purchases N lottery tickets. If each of the tickets he buys has (independently of the other tickets) the probability

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hw10 - ORIE 3500/5500 Engineering Probability and...

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