Can the expectation of a continuous random variable be negative?

Question

I'm given this pdf:

$f(y)= \frac{1}{2}(1-y^3), -1<y<1 , 0 $ elsewhere.

I've computed the expected value which gives $-\frac{1}{5}$ and I'm wondering if an expected value can actually be negative.
Any sort of help is appreciated. Thank you!

Answer 1

Consider a random variable $X$, with expectation $1$.

Now $Y:=X-2$ is also a random variable and has expectation $-1$.

Of course, the expectation of a non-negative random variable cannot be negative.