List of top Statistics Questions on Sampling Distributions

Let \(X_1,X_2,\ldots,X_n\) be a random sample of size \(n\;(n>1)\) from a \(N(\mu,1)\) distribution, where \(\mu\in\mathbb{R}\) is an unknown parameter. If \(\overline{X}=\frac{1}{n}\sum_{i=1}^{n}X_i\), then the minimum value of \(n\) such that

Let \(X_1,X_2,\ldots,X_9,Y\) be independent and identically distributed \(N(\mu,\sigma^2)\) random variables. Define

If \(X_1\) and \(X_2\) are two independent random variables having identical N(0, 1) distribution, then \(P(X_1^2 + X_2^2 \le 2)\) equals: