How do we derive that $S^2$ is chi-squared distributed (with $n-1$ df)?
92862
Degrees of freedom for standard deviation of sample
65784
If $X,Y$ are independent $\chi ^2$ with $m$ and $n$ degrees of freedom, then $\frac{X}{X+Y} \sim\beta(m/2, n/2)$
54731
Derivation of chi-squared pdf with one degree of freedom from normal distribution pdf
138349
How does Pearson's Chi Squared Statistic approximate a Chi Squared Distribution
40076
Correct Intuition? Standard Deviation and distance in $n$ dimensional space.
20153
What is the distribution of $R^2$ in linear regression under the null hypothesis? Why is its mode not at zero when $k>3$?
96036
If $X$ takes on a Gamma Distribution, how can I find $X^2$, $X^3$, etc?
81643
Proof that the hypergeometric distribution with large $N$ approaches the binomial distribution.
125991
Calculation of Pearson's Chi-squared statistic
81884
Minimal sufficient statistic of $\operatorname{Uniform}(-\theta,\theta)$
26604
Generalized Chi-Squared Distribution PDF
84185
density of $X^2$ when $X$ has uniform $[-1, 2]$ distribution
10482
Prove $(\sum_{i=1}^{n}X_{i},\sum_{i=1}^{n}X_{i}^{2})$ is not a complete statistic for $N(\mu,\mu^2)$ distribution
52693
Multivariate Hypergeometric Distribution with "or more" Successes
35967
Prove the order statistic is a minimal sufficient statistic for the logistic pdf $f(x|\theta)=\frac{e^{-(x-\theta)}}{(1+e^{-(x-\theta)})^2}$
141194
Prove that $\frac{(n-2)s^2}{\sigma^2}\sim \chi^{2}_{n-2}$
93185
asymptotic distribution of $\sqrt{n}(\hat\theta_n-\theta)$ to determine the efficiency of $\hat\theta_n$?