N people put their belongings in the jar one by one, and when they are picked...

N people put their belongings in the jar one by one, and when they are picked one arbitrarily, the number of people who choose their own things is called a random variable X.

a. If the i-th person chooses his belongings, Xi = 1, otherwise Xi = 0, explain whether the probability variable Xi can have a Bernoulli distribution, and mark the probability variable X as a function of Xi.

b. Show E(Xi) = 1 / N and Var(Xi) = (N - 1) / N^2.

c. Find the expected value of E (X) and the distributed Var (X) for choosing your belongings.

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Expert Solution

orchestra answered 1 year ago

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