Suppose that each coupon obtained is, independent of what has been previously obtained, equally likely to be any of $m$ different types. Find the expected number of coupons one needs to obtain in order to have at least one of each type. Hint: Let $X$ be the number needed. It is useful to represent $X$ by $$ X=\sum_{i=1}^{m} X_{i} $$ where each $X_{i}$ is a geometric random variable.
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We are looking for the expected number of coupons needed to obtain at least one of each type, which can be represented as $X = \sum_{i=1}^{m} X_i$. Show more…
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