Question: 3. Suppose random variable X1 Beta(a,b), and random variable K given X1 = x has a Binomial distribution, Bin(n,x). Suppose the random variable X2 given

3. Suppose random variable X1 Beta(a,b), and

3. Suppose random variable X1 Beta(a,b), and random variable K given X1 = x has a Binomial distribution, Bin(n,x). Suppose the random variable X2 given X1 = x and K = k has a Beta distribution, X2|(X1 = x, K = k) ~ Beta(k+a, n k +B). 10, a) Write a program to estimate Corr(X1, X2) from 1000 simulation runs when n= a = 8 and = 2. b) Find an expression for Corr(X1, X2). Hint E(X1X2) = Ex1(Ek|x, [Exz]K,x (X1X2)]). 3. Suppose random variable X1 Beta(a,b), and random variable K given X1 = x has a Binomial distribution, Bin(n,x). Suppose the random variable X2 given X1 = x and K = k has a Beta distribution, X2|(X1 = x, K = k) ~ Beta(k+a, n k +B). 10, a) Write a program to estimate Corr(X1, X2) from 1000 simulation runs when n= a = 8 and = 2. b) Find an expression for Corr(X1, X2). Hint E(X1X2) = Ex1(Ek|x, [Exz]K,x (X1X2)])

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