Refer to the Journal of Engineering for Industry (May 1993) study of friction feed paper separation, Exercise 5.12. Consider a system that utilizes two interrelated feed paper separators. The joint density of X and Y, the friction coefficients of the two machines, is given by

a. Verify that f(x, y) is a bivariate joint probability distribution function. [Show that Definition 6.4 holds for f (x, y).]
b. Find the probability that both friction coefficients exceed .8.

Data from Exercise 5.12

Researchers at the University of Rochester studied the friction that occurs in the paper feeding process of a photocopier (Journal of Engineering for Industry, May 1993). The coefficient of friction is a proportion that measures the degree of friction between two adjacent sheets of paper in the feeder stack. In one experiment, a triangular distribution was used to model the friction coefficient, Y. (See the accompanying figure.)

Transcribed Image Text:

if 0 sxs 1;0 s ys1 if 1 sxs 2;0 s ys1 if 0 sxs 1; 1 sys 2 (2 – x)(2 – y) if 1 sxs 2; 1 sys 2 ху (2 - x)y x(2 — у) f(x, y) =