Mean Cover Times for Coupon Collectors and Star Graphs
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Suppose that there are m distinct types of coupons and that each coupon collected is type; with probability P j , j = 1, ⋯, m. Let N k denote the number of coupons one needs to collect in order to have at least one of each of k distinct types. We are interested in using simulation to efficiently estimate the mean and variance of N k , for each k = 1, ⋯, m. Whereas we could simulate the successive types of coupons obtained and then utilize the observed values of N k over many runs to obtain our estimates, we will attempt to obtain estimators having smaller variances than these raw estimators.
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