Let X [cm 1 and Y [cm 1 be the diameter of a pin and hole.

Chapter 24, Problem 24.9

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Let X [cm 1 and Y [cm 1 be the diameter of a pin and hole. respectively. Suppose that (X, Y) has the density f(x, y) = 2500 if 0.99 < x < 1.01. 1.00 < Y < 1.02 and 0 otherwise. (a) Find the marginal distributions. (b) What is the probability that a pin chosen at random will fit a hole whose diameter is l.00?

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