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

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!...