Find (if it exists) random variable $X$ so it is vaild: $\mathbb{E}(X)= 3, \mathbb{E}(X^2) = 8$. Find (if it exists) random variable $X$ so it is vaild: $\mathbb{E}(X)= 3, \mathbb{E}(X^2) = 8$.
I tried by definition of expectation, but how can I know that, when squared, some values won't be same (which implies that new probability is sum of those probabilities).

Note that
$$
\text{Var}(X)=E(X-EX)^2=EX^2-(EX)^2=8-9=-1<0
$$
which is impossible. Hence such a random variable does not exist.
