Finding $E[X^2]$ where X is uniformly distributed random variable

Question

I'm trying to compute $E[X^2]$ where $X$ is a uniform $(0,3.3)$ random variable. This is what I tried:

$E[X^2] = \int_0^{3.3}x^2 f_X (x)$ where $f_X(x) = \frac{1}{3.3}$ whenever x $\epsilon (0,3.3)$ and $0$ otherwise.

This led me to a value of 3.63, which is unfortunately incorrect.

Is this, perhaps, not the correct method?

Answer 1

Hint: $\text{Var}(X) = E[(X-E[X])^2] = E[X^2] - E[X]^2.$ So if we know $X \sim U(a,b)$, then $E[X] = \frac{1}{2}(a+b)$ and $\text{Var}(X) = \frac{1}{12} (b-a)^2$.

Alternatively, you can do what you did. You'll actually get the same answer, so I'm curious what is going on.