| Photocapier friction. 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, . (See the accompanying figure.) f) Triangular friction distribution 1/c y p-c u H+c The density function for the triangular friction distribution is given by % ifuec 0. a. Show that [ o fiy)dy = 1 b. Find the mean of the triangular friction distribution. c. Find the variance of the triangular friction distribution. Show that the variance of a gamma distribution with parameters a and p is af?. Suppose a random variable Yhas a probability distribution given by RY) (cyley/ ify >0 elsewhere Find the value of c that makes f(y) a density function.| Verify that the moment generating function of a uniform random variable on the interval a) if 0 = x