What is the formula for this?

Question

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

Answer 1

Going back to definitions (always a good thing in math) V(x) or variance of a dataset x is equal to the sum of the squares of the errors (actual value minus expected value for each x) divided by n-1 where n = the number of the variables x.

V(x) = ∑(x_i - E(x))² / (n-1)

For a general beta distribution with parameters α & β this works out to

V(x) = αβ/((α+β)²•(α + β+1)) - this is the formula for calculating the Variance of a Beta distributed variable.

For alpha =. 5 and beta = 2 we get 5*2/(7² * 8). or .02551

Source of variance function for Beta distribution was

https://en.wikipedia.org/wiki/Beta_distribution#:~:text=of%20statistical%20dispersion-,Variance,monotonically%20as%20%CE%B1%20%3D%20%CE%B2%20increases.