The route that Jackie follows to school each day includes eight stoplights. When she reaches each stoplight, the probability that the stoplight is red is 0.25 and it is assumed that the stoplights are spaced far enough apart so as to operate independently. If the random variable Z counts the number of red stoplights Jackie encounters one particular day on her ride to school, determine
(a) Pr(X = 0).
(b) Pr(X = 3).
(c) Pr(X > 6).
(d) Pr(X > 6|Z > 4).
(e) E(X).
(f) Var(X).