# Let X [cm] and Y [cm] be the diameters of a pin and hole, respectively. Suppose that (X, Y) has the density f(x, y) = 625 if 0.98 < x < 1.02, 1.00 < y < 1.04 and 0 otherwise. (a) Find the marginal distributions. (b) What is the probability that a pin chosen at random will fit a hole

Chapter 24, PROBLEM SET 24.9 #8

Let X [cm] and Y [cm] be the diameters of a pin and hole, respectively. Suppose that (X, Y) has the density

f(x, y) = 625 if 0.98 < x < 1.02, 1.00 < y < 1.04

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 1.00?

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