Problem 4. (+20pts) An experiment results in 2 independent equally likely outcomes from the set of values {-1, 0, 1}. Let X be a discrete random variable defined as the sum X =Y+Z2, Y = the first outcome, Z = the second outcome, (a) List the sample space S and values of X, Y, Z on each of these simple outcome in S. (b) Compute the pdf of the random variable X i.e. f(x) = P(X = x). Write the values of f(x) in a table. (c) Based on f(x) draw a "staircase graph" of the cumulative distribution function F(x) = P(X