5. A discrete random variable X has the following probability mass function (pmf):
p0 = 0.2, p2 = 0.05, p3.5 = 0.3, p5 = 0.25, p6 = 0.2
(a) State the support of X, Sx.
(b) Determine the cdf of X, Fx.
(c) Use the cdf, Fx, to calculate P(2 < X < 5). (Use 1.interval)
(d) Use the pmf, p(x), to calculate P(2 < X < 5) and P(2 < X ≤ 5). How are they different?
(e) Use the cdf, Fx, to calculate P(2.5 < X ≤ 5) and P(2.5 < X < 5). How are they different?
(f) Calculate the expectation, E(X). Find out E(3X - 5X^2 + 7). What is E(5)?
(g) What is the expression of Var(X) in this problem if you use the definition of Var(X) = E{X - E(X)}? Alternatively, use Var(X) = E(X^2) - {E(X)} to calculate Var(X). What is Var(-3X + 5)?