Suppose X Uniform It is given that EX 2 and VarX 025 What

Suppose X Uniform[, ]. It is given that E(X) = 2 and Var(X) = 0.25. What are the values of and for this uniform distribution?

Solution

As

E(x) = (a + b)/2 = 2

Var(x) = (1/12)(b - a)^2 = 0.25

Then

a + b = 4

b - a = 1.732050808

Thus,

a = 1.133974596

b = 2.866025404 [ANSWERS]