4-12. Let a random variable X be defined as the number of heads obtained in two flips of a fair coin. Determine the sample space S and the associated

(discrete) probability distribution. Verify that the sequence of probabilities can be determined from the probability mass function f (X) =

⎧⎪⎪⎨

⎪⎪⎩

52 X

6 4 , X = 0, 1, 2;

0 elsewhere.

Given f (X) find the cumulative distribution function.