Suppose X has a uniform distribution over the points {1, 2, 3, 4, 5, 6} and that g(x) = sin(π 2 x). a. Determine the distribution of Y = g(X) = sin(π 2 X), that is, specify the values Y can take and...

Suppose X has a uniform distribution over the points {1, 2, 3, 4, 5, 6} and that g(x) = sin(π 2 x). a. Determine the distribution of Y = g(X) = sin(π 2 X), that is, specify the values Y can take and give the corresponding probabilities.

b. Let Z = cos( π 2 X). Determine the distribution of Z.

c. Determine the distribution of W = Y 2 + Z². Warning: in this example there is a very special dependency between Y and Z, and in general it is much harder to determine the distribution of a random variable that is a function of two other random variables. This is the subject of Chapter 11.