(problem from an old actuarial exam) an actuary models the lifetime of a device using the random variable y = 10x0: 8, where x is an exponential random variable with mean 1 year. determine the probability density function f(y), for y > 0, of the random variable y . (it might be to derive the c. d.f. of y and then take a derivative to nd the density.)

At the county fair, animals are judged for the quality of their breeding and health. the animal pens are arranged in an array, with one animal in each pen. a barn can hold at most 10 rows of pens and at most 6 pens in each row, with room for people to walk around them. what different ways can the planners of the county fair arrange the pens for the horses and cows in the same barn?