For each of the following, determine the constant c so that f(x) satisfies the conditions of being a p.m.f. for a random variable X, and then depict p.m.f. as a bar graph.
An unbiased four-sided die X has two faces numbered 0 and two faces numbered 2. An unbiased four-sided die Y has its faces numbered 0, 1, 4, and 5. Two dices are rolled. Let W = X + Y.
a) Determine the p.m.f. of W.
b) Draw a probability histogram of the p.m.f. of W.
The solution contains an application of probability distribution.