Random variable such that $E[X^2] = 20$
My professor told me that the mean and variance are the same size. I now have to find that size. I am under the assumption that it's one, because I would conclude that the variance squared should be one if it was one before. Any help is appreciated.
Use the definition of Variance, $$\mathsf {Var}(X)=\mathsf E[X^2]-\mathsf E[X]^2$$
... and if variance and mean are equal to $x$ then
$$x=20-x^2$$
$$x^2+x-20=0$$