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Problem 2 - Textbook- A first course in Probability- Sheldon Ross- Pro.pdf

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Problem 2 , Textbook: A first course in Probability, Sheldon Ross. Problem 2. Let U be a uniform random variable. Suppose that the conditional distribution of X given that U = p is binomial with parameters n and p . a.) Give an intuitive explanation that the probability mass function of X is P { X = i } = n + 1 1 b.) Prove this. (You are allowed to assume that 0 1 p i ( 1 p ) n i d p = ( n + 1 )! i ! ( n i )! . ).

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Problem 2 , Textbook: A first course in Probability, Sheldon Ross. Problem 2. Let U be a uniform random variable. Suppose that the conditional distribution of X given that U = p is binomial with parameters n and p . a.) Give an intuitive explanation that the probability mass function of X is P { X = i } = n + 1 1 b.) Prove this. (You are allowed to assume that 0 1 p i ( 1 p ) n i d p = ( n + 1 )! i ! ( n i )! . )

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