List of top Statistics Questions on Exponential distribution

Let \(X_1,X_2,X_3\) be a random sample of size \(3\) from \(Exp(1)\) distribution. Then, \(E\left(4X_{(2)}e^{X_{(2)}}\right)\) equals (in integer).

Let \(X_1,X_2,\ldots,X_n\) be a random sample of size \(n\;(n>1)\) from an \(Exp(\beta)\) distribution, where \(\beta>0\). If \(T=\sum_{i=1}^{n}X_i\), then which of the following statements is/are true?

Let \(X_1,X_2,\ldots,X_{10}\) be a random sample of size \(10\) from an \(Exp(\beta)\) distribution, where \(\beta>0\) is an unknown parameter. Let