Can we have a random variable with EX 3 and EX2 8SolutionDo

Can we have a random variable with E(X) =3 and E(X)^2 =8?

Solution

Do you mean E(X^2) = 8?

If so, note that

Variance = E(X^2) - E(X)^2

Thus, in this case,

Variance = 8 - 3^2 = -1

However, the variance can never be negative, as it is a squared value of the standard deviation.

Thus, THIS IS IMPOSSIBLE, E(X) = 3 and E(X^2) = 8 cannot happen.