A scientist suggests that X ∼ Beta(α = 5, β = 2) is a good model for the proportion of surface area in a randomly selected quadrat that is covered by a certain plant that she is studying. Assuming this model is (approximately) correct, compute the following:
a) E(X) and Var(X),
b) the median of X,
c) P(X ≤ E(X)),
d) P(0.2 ≤ X ≤ 0.4),
e) the probability that X is within 1 standard deviation of the mean.