📘 probability and statistics

1. **Problem a**: Develop a formula for a random variate generator for the random variable $X$ with p.d.f. $$f(x) = \begin{cases} e^{2x} & -\infty < x \leq 0 \\ e^{-2x} & 0 < x < \

1. **Problem statement:** (a) Transform random numbers uniform on $[0,1]$ to uniform on $[-11,17]$.

1. **Problem Statement:** We have three random variables \(X, Y, Z\) with normal distributions: - \(X \sim N(100, 100)\), meaning mean \(\mu_X = 100\) and variance \(\sigma_X^2 = 1

1. The problem appears to involve probability and statistics concepts in the context of a category or assessment. 2. Since no specific question or data is provided, I will explain