Geneticist D. N. Hay has been experimenting with two types of mice, light-haired mice cloned from a particularly hearty species and dark-haired mice that are direct descendants of a well-known mouse named Mickey. Assume that X and Y are, respectively, the pro- portion of each of these two types of mice that exit a specially designed maze within three minutes. Over many experiments with different batches of these mice, the variables X and Y have been found to be well-modeled by the joint density fx. y(x, y)-kr(1 - y) for O (a) Find the value of k for which f(x, y) is a valid bivariate density.
(b) Find the expected value of the ratio Y/X.
(c) Evaluate the probability that X+Y s1.