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1. (Poisson Approximation in Hoppe's Urn). Consider a Hoppe urn with () D 1. Find the exact distribution of S10 and also a suitable Poisson approx- imation. Compare them. Why do you think that a Poisson approximation is worth considering?

2. (Size of the Oldest Species). In Hoppe's urn scheme, let Zn denote the number of animals of the oldest species after n iterations. Find a closed-form formula for the mean and the variance of Zn for a general ().

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