Now I am really struggling to understand the definition of the mean squared error.
The question I am working on:
$X\sim \operatorname{Bin}(n,\pi)$. Find the mean squared error of the estimators $\widehat{\pi}=\frac{X}{n}$ and $\stackrel\sim \pi = \frac{X+1}{n+2}$.
Given that $E(X)=n\pi$ and $\operatorname{var}(X)=n\pi(1-\pi)$.
I am trying to get my head around the notation used in the definition of the MSE.
Now the bias is the expectation of $X$ minus $\pi$? Then the MSE would be the given variance plus the bias squared? Any help would be appreciated.