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MIT6_041F10_assn07

# MIT6_041F10_assn07 - Massachusetts Institute of Technology...

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Massachusetts Institute of Technology Department of Electrical Engineering & Computer Science 6.041/6.431: Probabilistic Systems Analysis (Fall 2010) Problem Set 7 Due November 8, 2010 1. Consider a sequence of mutually independent, identically distributed, probabilistic trials. Any particular trial results in either a success (with probability p ) or a failure. (a) Obtain a simple expression for the probability that the i th success occurs before the j th failure. You may leave your answer in the form of a summation. (b) Determine the expected value and variance of the number of successes which occur before the j th failure. (c) Let L 17 be described by a Pascal PMF of order 17. Find the numerical values of a and b in the following equation. Explain your work. a b p L 17 ( l ) = p x (1 p ) ( b x ) x l =42 x =0 2. Fred is giving out samples of dog food. He makes calls door to door, but he leaves a sample (one can) only on those calls for which the door is answered and a dog is in residence. On any call the probability of the door being answered is 3 / 4, and the probability that any household has a dog is 2 / 3. Assume that the events “Door answered” and “A dog lives here” are independent and also that the outcomes of all calls are independent. (a) Determine the probability that Fred gives away his first sample on his third call.

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MIT6_041F10_assn07 - Massachusetts Institute of Technology...

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