Implement Sampling and Minimize Loss in Numerical Coding

Scenario

Numerical coding challenges on sampling and loss minimization.

Question

a) Implement functions to sample from truncated normal distributions for x>1, 4<x<4.05, and x>4. b) For an array X, find the value minimizing Σ(x−θ)², then the value minimizing Σ|x−θ|, and derive the loss that yields the 90th percentile.

Hints

Use rejection or CDF-inverse methods; derivatives show mean, median, and quantile solutions.