Exercise 3. (Random Variables, PMF) (25pt). Let the sample space be given by S = {HH, TT, TH, HT} with probability assignments given by P({HH}) = , P({TT}) = P({TH}) = Moreover, let the random variable Y be defined as follows: Y = {number of tails in an outcome}, and the random variable X be defined as follows: X = {number of heads - number of tails}. (a) What is the probability assignment for P({HT})? (b) What is the range of random variable Y? (c) Find the probability mass function (pmf) of Y? (d) Draw a line graph for the pmf of Y. (e) What is the range of random variable X? (f) Find the pmf of X. (g) Draw a line graph for the pmf of X