Question

Assume X and Y are random variables with both have mean 3 and variance 2. Calculate E left square bracket X squared plus 4 Y minus 5 right square bracket. (Hint: Think how to calculateE left square bracket X squared right square bracket given the mean and the variance).

Answer 1

E[X² + 4Y - 5] = 18

Explanation:

Mean = E(X) = 3

E(Y) = 3

Variance = Var(X) = 2

Var(Y) = 2

Calculate E[X² + 4Y - 5]

E[X² + 4Y - 5] = E(X²) + 4E(Y) - E(5)

But Var(X) = E(X²) - [E(X)]²

E(X²) = Var(X) + [E(X)]² = 2 + 3² = 2 + 9 = 11

E(5) = 5

E[X² + 4Y - 5] = E(X²) + 4E(Y) - E(5) = 11 + 4(3) - 5 = 11 + 12 - 5 = 18

Hope this Helps!!!