Let f1 and f2 be the probability functions of two discrete random variables with the same range RX and 0 ≤ ???? ≤ 1 be a real number. Verify that the function f (x) = ????f1(x) + (1 − ????)f2(x), x ∈ RX, defines a probability function on RX. Observe that this is the probability function of the two-component mixture distribution mentioned in Exercise 12 of Section 4.2.