Show transcribed image text numbers from the set of two elements (1, 2) at random and with replacement. Let X be the sum of the two numbers. a. (5 pts) What are possible values of X? b. (9 pts) Derive the probability mass function (pmf) of X. c.(5 pts) Let F(x) be the cumulative distribution function of X. Find F(3).

numbers from the set of two elements (1, 2) at random and with replacement. Let X be the sum of the two numbers. a. (5 pts) What are possible values of X? b. (9 pts) Derive the probability mass function (pmf) of X. c.(5 pts) Let F(x) be the cumulative distribution function of X. Find F(3).