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Statistics
MSE of sample standard deviation (cont')
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.
Apr 20, 2023
1 min read
Statistics
MSE of sample standard deviation
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.
Apr 19, 2023
2 min read
Statistics
MSE of sample variance
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}.
Aug 1, 2020
3 min read
Statistics
Variance of sample mean squared
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.
Aug 1, 2020
2 min read
Statistics
Girl ratio
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.
Sep 10, 2017
1 min read
Statistics
Two cool things about dice!
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?
Apr 14, 2016
1 min read
Statistics