Exponential distribution solving X^2, lambda value known

Question

Let $X$ be a random variable with exponential distribution with parameter $\lambda=2$. The expectation of the random variable $Y=X^2$ is equal to

a) 1/2

b) $\sqrt{2}/2$

c) 1

d) 2

e) 4

I've done this. $$\mathbb{E}(x)=\frac{1}{\lambda} \implies \mathbb{E} = \frac{1}{\lambda}=0.5.$$ Should I now do some kind of integration using $\mathbb{E}(X^2)$ or some other approach?

Answer 1

HINT

If $X$ is a random variable with pdf $f(x)$ then $$ \mathbb{E}[g(X)] = \int_{-\infty}^\infty g(x) f(x) dx. $$

Can you apply this to your problem? What is $g(x)$? Can you integrate?