The following paper does a variety of interesting probabilistic analyses: P. Flajolet et.al., “Birthday paradox, coupon collectors, caching algorithms and self-organizing search”, Discrete Applied Mathematics 39 (1992), 207-229. ( http://algo.inria.fr/flajolet/Publications/FlGaTh92.pdf ) It includes the following formula, which provides the expected number of coupons needed under a general discrete probability distribution P for m coupons: (14b) where For m=3 and , the paper simplifies (14b) to: . Your task is write a C program to 1) evaluate (14b) for the special case that k of the probabilities are the value p and the other m – k probabilities are the value q and 2) implement a simple random simulation of generating coupons for this situation. Your program must compile and execute on omega.uta.edu. (Formula (1) in https://web.cs.wpi.edu/~hofri/CCP.pdf says essentially the same thing as the formula above.)
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