Question

If X~Uni(0,5), then Var(3x - 111) is

Answer 1

The variance of the transformed variable 3X - 111, where X follows U(0, 5), is 18.75.

Step-by-step explanation:

To find the variance of the linear transformation of a uniform distribution, we use the formula Var(aX + b) = a2Var(X) where a and b are constants, and X is a random variable.

Given that X follows a uniform distribution U(0, 5), the variance of X, denoted as Var(X), is calculated using the formula Var(X) = (b - a)2 / 12 where a and b are the minimum and maximum values of the uniform distribution respectively.

In this case, for X ~ U(0, 5), the variance would be:

• Var(X) = (5 - 0)2 / 12 = 25 / 12

Now, for the transformed variable 3X - 111, we apply:

• Var(3X - 111) = 32Var(X) = 9 * (25 / 12) = 225 / 12 = 18.75