Help answering this statistics problem.?

Question

Suppose that X is random variable with a mean of 5 and a variance of 9. If y = 2x^2 + 4, find the mean of Y.

I used the equation variance = e(x^2) - [e(x)]^2

9 = mean(y) - 5^2,
34 = mean(y)

The answer in the book is 72. Can somebody help me?

Answer 1

mean of Y = E[Y] = E[2X² + 4] = 2E[X²] + E[4] = 2E[X²] + 4

Now, you correctly note that variance = E[X²] - (E[X])² so

E[X²] = variance + mean² = 9 + 25 = 34

Then E[Y] = 2E[X²] + 4 = 2*34 + 4 = 72