題組內容

2. (5% each, totally 15%) Let X be the amount of time walking from a park to another. There are two paths between the two parks, denoted by H₁ and H₂. If path H₁ is chosen, then X is the exponential random variable, with the mean of 10 minutes. If path H₂ is chosen, then X is the exponential random variable, with the mean of 20 minutes.

(a) What is the conditional PDF \( f_{X|H_1}(x) \) given path \( H_{1} \) is chosen?