What is the formula for calculating this?

Question

X follows a beta distribution with parameters alpha=5 and beta=2. What is V(X)?

Answer 1

If by V(X) is meant the Variance of X (with X Beta Distributed), one would write:

V(X) = σ² =

αβ

------------------------- .

(α + β)²(α + β + 1)

For α = 5 and β = 2, the Variance or σ² or V(X) would then be (5 × 2) divided by (5 + 2)²

divided by (5 + 2 +1) or 10 ÷ 49 ÷ 8 or 5/196.

Note that the Mean or µ or E(X) here is given by α/(α + β) or 5/(5 + 2) or 5/7.