Let Y be a normal random variables, with mean 3 and variance 16.

Question

Let V = (4-Y)/3

Find the variance of V

Answer 1

First, we need to find the mean of V:

E(V) = E[(4-Y)/3] = 4/3 - E(Y)/3 = 4/3 - 3/3 = 1/3

Next, we can use the formula for the variance of a linear transformation of a random variable:

Var(aX + b) = a^2Var(X)

In this case, a = 1/3 and b = 4/3, so:

Var(V) = Var[(4-Y)/3]
= (1/3)^2Var(Y)
= (1/9)(16)
= 16/9

Therefore, the variance of V is 16/9.