Statistics

Continue our previous post of computing the MSE of sample standard deviation. We want to have higher order expansion of $E(S_n)$. The algebric computation is a bit tedious, we will use sympy to help us.

In a previous post, we have discussed the MSE of sample variance. One could argue that we should compute the MSE of the sample standard deviation as sample s.d. has the same unit as the measurements.

In introductory statistics courses, we often focus on unbiased estimators such as the sample variance, $$ S^2 = \frac{\sum(X_i - \bar X)^2}{n - 1} $$ rather than a more initiative estimator $$ \hat \sigma^2 = \frac{\sum(X_i - \bar X)^2}{n}.

It is well known that $\bar X^2$ is a biased estimator for $\mu^2$, but how about its variance? Before we start working on $Var(\bar X^2)$, let’s recall that $\bar X$ is an unbiased estimator for $\mu$, i.

https://stats.stackexchange.com/questions/93830/expected-number-of-ratio-of-girls-vs-boys-birth The Zorganian Republic has some very strange customs. Couples only wish to have female children as only females can inherit the family’s wealth, so if they have a male child they keep having more children until they have a girl.

Just discover two cool things about dice, Suppose we have two (fair) 6-sided dice, let $Y$ be the reminder of the product of the two numbers divided by 7, i.e., $Y = X1 \times X2 (\text{ mod } 7)$, guess what the distribution of $Y$ is?