Suppose that X and Y are discrete random variables with a
Chapter , Problem 40(choose chapter or problem)
Suppose that X and Y are discrete random variables with a joint probability mass function \(p_{XY}(x, y)\). Show that the following procedure generates a random variable \(X \sim p_{X|Y} (x|y)\).
a. Generate \(X \sim p_X (x)\).
b. Accept X with probability p(y|X).
c. If X is accepted, terminate and return X. Otherwise go to Step a.
Now suppose that X is uniformly distributed on the integers 1, 2, . . . , 100 and that given X = x, Y is uniform on the integers 1, 2, . . . , x. You observe Y = 44. What does this tell you about X? Simulate the distribution of X, given Y = 44, 1000 times and make a histogram of the value obtained. How would you estimate E(X|Y = 44)?
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