Question

Given x~U(5, 15), what is the variance of x?

Answer 1

To find the variance of a continuous random variable x with a uniform distribution U(a, b), you can use the formula:

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

In this case, x follows a uniform distribution U(5, 15), where a = 5 and b = 15. Plugging these values into the formula, we get:

Var(x) = (15 - 5)^2 / 12
= 10^2 / 12
= 100 / 12
≈ 8.3333

Therefore, the variance of x is approximately 8.3333.