### Questions (57)

 11 How can I obtain a Cauchy distribution from two standard normal distributions? 10 What distribution does the mean of a random sample from a Uniform distribution follow? 9 How can I find the distribution for the number of years until the first year's rainfall is exceeded for the first time? 7 How do I show that $Y=2\sqrt{X_1X_2}\sim$Gamma$(2p,1)$? 6 How can I find the asymptotic variance of the MLE of $\beta$ for $f_y(y|\beta,\mathbf{x})=\frac{\beta x}{1+\beta x}(\frac{1}{1+\beta x})^{y-1}$?

### Reputation (1,585)

 +10 What distribution does the mean of a random sample from a Uniform distribution follow? +10 How can I show that the LRT of $H_0:\theta_0=\theta_1=...=\theta_k$ is given by the F test under one-way ANOVA assumptions? +30 How can I obtain a Cauchy distribution from two standard normal distributions? +10 Is there a way to prove $\mathbf{\hat{Y}}^T\mathbf{e}=\mathbf{0}$ without resorting to summations?

 1 How can I find the BUE of $\theta$ in the simple linear relationship $Y_i=\theta x_i^2+\epsilon_i$? 1 How can I find $c$ such that $c(X_1-X_2)/ \sqrt{X_3^2 +X_4^2 + X_5^2}$ forms a t distribution? 0 How to study statistics 0 How can I find an unbiased estimator for $\frac{1-\theta}{\theta}$ to obtain this quantity's UMVUE? 0 What is an appropriate transformation for the response variable "size"?

### Tags (70)

 2 mathematical-statistics × 49 1 regression × 3 1 distributions × 11 1 t-distribution × 2 1 normal-distribution × 8 1 linear × 2 1 umvue × 4 0 self-study × 30 1 unbiased-estimator × 4 0 probability × 11

### Bookmarks (2)

 51 Consider the sum of $n$ uniform distributions on $[0,1]$, or $Z_n$. Why does the cusp in the PDF of $Z_n$ disappear for $n \geq 3$? 4 MLE for 2 parameter exponential distribution