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Suppose that the random variable Y has a binomial distribution with n trials and success probability X, where n is a given constant and X

Suppose that the random variable Y has a binomial distribution with n trials and success probability X, where n is a given constant and X is a uniform (0,1) random variable.

  • Find EY and Var Y
  • Find the joint distribution of X and Y
  • Find the marginal distribution of Y

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