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# compexp - Class Problems Computing Expectations(discrete 1...

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Class Problems: Computing Expectations (discrete) 1. Compute the expected value of a binomial random variable with paramaters n and p by writing it down as a sum of n Bernoulli random variables. 2. The following problem was posed and solved in the 18th century by Daniel Bernoulli. Suppose that a jar contains 2 N cards, two of them marked 1, two marked 2, two marked 3, and so on. Draw out m cards at random. What is the expected number of pairs that still remain in the jar? (Interestingly enough, Bernoulli proposed the above as a possible probabilistic model for determining the number of marriages that remain intact when there are a total of m deaths among N married couples.) 3. A group of N people throw hats into the center of a room. The hats are mixed up, and each person randomly selects one. Find the expected number of people that select their own hats. 4. If n balls are randomly selected from an urn containing N balls of which m are white, find the expected number of white balls selected.

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compexp - Class Problems Computing Expectations(discrete 1...

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