Counting heads. Given integers n and k, along with p1,..., pn ∈ [0,1], you want to determine the probability of obtaining exactly k heads when n biased coins are tossed independently at random, where pi is the probability that the ith coin comes up heads. Give an O (nk) algorithm for this task.2 Assume you can multiply and add two numbers in [0,1] in O (1) time.
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