# hw2-2011 - p is flipped 10 times Given that a total of 6...

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Theory of Probability, HW #2, all sections Assignment Date: March 18, 2011; Due Date: March 25, 2011 1. The Celtics and the Lakers are set to play a playoff series of n basketball games, where n is odd. The Celtics have a probability p of winning any one game, independently of other games. Find the values of p for which n = 5 is better for the Celtics than n = 3. 2. If X is a Poisson random variable with parameter λ , show that E [ X n ] = λ E [( X + 1) n -1 ] Now use this result to compute E [ X 3 ]. 3. A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win \$1.10; if they are different colors then you lose \$1.00. Calculate a. the expected value of the amount you win; b. the variance of the amount you win. 4. Suppose that a biased coin that lands on heads with probability
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Unformatted text preview: p is flipped 10 times. Given that a total of 6 heads result, find the conditional probability that the first 3 outcomes are a. h , t , t (meaning that the first flip is heads, the second is tails and the third is tails); b. t , h , t . 5. How many people are needed so that the probability that at least one of them has the same birthday as you is greater than ½? Solve it by using random variable properties. 6. A newsboy purchases papers at 10 cents and sells them at 15 cents. However, he is not allowed to return unsold papers. If his daily demand is a binomial random variable with n = 10, p = 1/3, approximately how many papers should he purchase so as to maximize his expected profit?...
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## This note was uploaded on 05/12/2011 for the course INDUSTRIAL 321 taught by Professor Memet during the Spring '11 term at Mitchell Technical Institute.

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