Expected value of the minimum of two standard half-normal distributions

1 · Andrey Akinshin · May 3, 2022, 9:48 a.m.
Let \(X_1, X_2\) be i.i.d. random variables that follow the standard normal distribution \(\mathcal{N}(0,1^2)\). One day I wondered, what is the expected value of \(Z = \min(|X_1|, |X_2|)\)? It turned out to be a fun exercise. Let’s solve it together!...