Exercise C.3.8
Which is larger: The expectation of the square of a random variable, or the square of its expectation?
We know that:
$$ \E[f(X)] \ge f(\E[X]) $$
If $f(x) = x^2$:
$$ \E[X^2] \ge \E^2[X] $$
The expectation of the square is larger.
Which is larger: The expectation of the square of a random variable, or the square of its expectation?
We know that:
$$ \E[f(X)] \ge f(\E[X]) $$
If $f(x) = x^2$:
$$ \E[X^2] \ge \E^2[X] $$
The expectation of the square is larger.