Let S be a given set consisting of n distinct items. A new set T is constructed as follows. In each step, an item is chosen at random from the set S (with replacement) and a copy of the item is added to the set T. What is the expected value of the number of distinct items in the set T after n steps?

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.2: Probability
Problem 2E
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Let S be a given set consisting of n distinct items. A new set T is constructed as follows. In each step, an item is chosen at random from the set S (with replacement) and a copy of the item is added to the set T. What is the expected value of the number of distinct items in the set T after n steps?

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