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Unformatted text preview: 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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This note was uploaded on 01/11/2012 for the course EE 6.431 taught by Professor Prof.dimitribertsekas during the Fall '10 term at MIT.
- Fall '10
- Electrical Engineering