Ok, so I have this question:

Suppose a continuous random variable

**X** is such that

**E(X) = 4 **and

**Var(X) = 7**. Suppose that Y is related to X by the rule

**Y=3X-2** Find

- E(Y)
- Var(Y)
- SD(Y)
- E(X2)
- E(Y2)

I calculated (or rather deducted )that E(X2) is 23. But how on earth am I supposed to calculate all these values of Y if I don't have the values of X?

I know that E[g(X)] = ∫g(x)f(x) dx, hence E(X2) = ∫x2.f(x) dx, but i don't have the f(x) values and I don't know how to calculate them from the given E(X) and Var(X) values. Please help