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.

(c) Suppose that a student chooses the two paths equal-likely. What is the expected value of \( X \) for the student?