Two methods of measuring surface smoothness are used to evaluate a paper product. The measurements are recorded as deviations from the nominal surface smoothness in coded units. The joint probability distribution of the two measurements is a uniform distribution over the region 0 < x < 4 < y, and x - 1 < y < x + 1. That is, fxy(x, y) = c for x and y in the region. Determine the value for c such that fxy(x, y) is a joint probability density function. Determine the following: a. P(X < 0.5, Y < 0.5) b. P(X < 0.5) c. E(X) d. E(Y) e. Marginal probability distribution of X f. Conditional probability distribution of Y given X = 1 g. E(Y | X = 1) h. P(Y < 0.5 | X = 1)