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Unformatted text preview: CS112  Homework #3 1. Consider that at a particular time of day t , there are 20 people active on a cellphone network of YMobile. At that particular time t, the probability that each of these 20 people are making a phone call independent to the behavior of all other active people is 0.2. We are interested in the number of simultaneous phone calls in the network at time t . (a) Define a random variable (say X ) that describes the scenario above. (b) What is the PMF of X ? (c) What is the probability that there are 4 simultaneous calls at time t ? 2. Let X be a gemoetrically distributed random variable with parameters p = 0 . 2 and q = 0 . 8. (i.e., p X ( k ) = (0 . 8) k 1 (0 . 2), for k = 1 , 2 , 3 ,... ) Let Y be another random variable with a slightly different PMF: p Y (1) = 0 . 18, p Y (2) = 0 . 18, p Y ( k ) = (0 . 8) k 1 (0 . 2), for k = 3 , 4 , 5 ,... . (a) Check if the PMF for Y is valid, i.e., check if ∑ ∞ k =1 p Y ( k ) = 1. (b) Compute P ( X = 4) and P ( X = 5  X ≥ 2). Are they same? Can you explain the answer using the memoryless property?...
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 Spring '08
 staff
 Probability theory, CPU time, cell phone traﬃc

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