Exercise 2.4. For the spring semester next year, you believe that the travel time to the...

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Exercise 2.4. For the spring semester next year, you believe that the travel time to the university will be between 10 and 15 minutes if the day is sunny and between 20 and 30 minutes if the day is rainy. Accordingly, you assume that the PDF of the travel time takes the following form: C₁, f(x)=C₂, 0, for constants C₁ and C₂. Your experience also suggests that the probability of a sunny day will be 1/4 during that semester. Find (1) the PDF of f(x) by solving for C₁ and C2, and (2) the mean and variance of your travel time. 10≤x≤ 15, 20≤x≤ 30, otherwise, Exercise 2.4. For the spring semester next year, you believe that the travel time to the university will be between 10 and 15 minutes if the day is sunny and between 20 and 30 minutes if the day is rainy. Accordingly, you assume that the PDF of the travel time takes the following form: C₁, f(x)=C₂, 0, for constants C₁ and C₂. Your experience also suggests that the probability of a sunny day will be 1/4 during that semester. Find (1) the PDF of f(x) by solving for C₁ and C2, and (2) the mean and variance of your travel time. 10≤x≤ 15, 20≤x≤ 30, otherwise,