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)= kx^2(1 - y) for 0 < x < 1 and 0 < y < 1

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 <= 1.