6 10 points A trucker drives between fixed locations in Broo

6. (10 points) A trucker drives between fixed locations in Brookings, South Dakota, and Kansas City, Missouri. The duration in hours, of a round trip, has an Exponential distribution with parameter beta = 12. Derive the probability that a round trip takes at most 25 hours given that it exceeds 10 hours.

Solution

6)

Note that

P(at most 25|exceeds 10) = P(10<x<25) / P(x>10)

Here, as B = 12,

P(10<x<25) = exp(-10/12) - exp(-25/12) = 0.310083737

P(x > 10) = exp(-10/12) = 0.434598209

Hence,

P(at most 25|exceeds 10) = 0.713495203 [ANSWER]