Let x denote the number of red marbles in the sample

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Unformatted text preview: 8. Suppose that Y denotes a number chosen at random from the set {1, 4, 7, 10, 13,, 295} . Find the mean and variance of Y. 9. Two players play a game to 5 points. The first player has probability 0.7 of winning any particular point. Currently, the second player leads 3 – 2. What is the probability that the first player wins? 10. A basketball player can hit a free throw 40% of the time. Let X equal the number of free throws the player hits in 20 shots. (a). What is the mean of X (b). What is the variance of X? (c). What is the probability he hits exactly 4 of the 20 shots? (d). What is the smallest number of shots must the player take in order to have a better than 80% chance of hitting at least one of them? (Express your answer in terms of natural logs.) 11. Suppose that you choose 10 marbles from a box containing 2000 red and 8000 blue marbles. Let X denote the number of red marbles in the sample. Use a Poisson approximation to X to evaluate P (1 ≤ X ≤ 3) . 12. Suppose that you roll a die until you get one of the patterns 65, 64, 63, 62, or 61. In other words you roll the die until you get a 6 followed immediately by a number other than 6. Let X denote the number of rolls...
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This note was uploaded on 01/25/2014 for the course MATH 511 taught by Professor Sumner during the Spring '13 term at South Carolina.

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