The lifetime of a certain type of vacuum tube is modeled by X ∼ Weibull(α = 2, β = 3). Compute the following:
a) E(X) and Var(X),
b) the median of X,
c) P(X ≤ E(X)),
d) P(1.5 ≤ X ≤ 6),
e) the probability that X is within 1 standard deviation of the mean.