In an urn containing n balls, the ith ball has weight W(i), i = 1, . . . , n. The balls are removed without replacement, one at a time, according to the following rule: At each selection, the probability that a given ball in the urn is chosen is equal to its weight divided by the sum of the weights remaining in the urn. For instance, if at some time i1, . . . , ir is the set of balls remaining in the urn, then the next selection will be ij with probability
Compute the expected number of balls that are withdrawn before ball number 1 is removed.
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