Thread: Help - continuous random variables...

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

1. E(Y)
2. Var(Y)
3. SD(Y)
4. E(X2)
5. 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

Originally Posted by Cassiopea

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

1. E(Y)
2. Var(Y)
3. SD(Y)
4. E(X2)
5. 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

E(aX + b) = a E(X) + b.

Var(aX + b) = a^2 Var(X) and sd(aX + b) = |a| sd(X).

Var(X) = E(X^2) - [E(X)]^2 therefore E(X^2) = Var(X) + [E(X)]^2.