Data Science Interview Prep: Q78

Expected Number of Distinct Elements — Sampling with Replacement. (Category: Statistics)

Let S = {1,2,3,…,n} be a set of n numbers. We draw n elements from S independently and uniformly at random with replacement. What is the expected number of distinct elements obtained in these draws?

Solution:

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Reference:

• Expected Number of Distinct Values in Sampling with Replacement: https://math.stackexchange.com/questions/4491807/expected-number-of-distinct-objects-in-sampling-with-replacement