Question: For low-risk drivers, the waiting time for their first accident follows an Exponential distribution with a mean of 7 years. For high-risk drivers, the waiting

For low-risk drivers, the waiting time for their first accident follows an Exponential with a mean of 7 years. For high-risk drivers, the waiting time for their first accident follows an Exponential with a mean of 2 years. Assuming that low-risk drivers and high-risk drivers are independent,
a. What is the probability that a low-risk driver and a high-risk driver will both have their first accident within the next 3 years?
b. What is the probability that either a low-risk driver or a high-risk driver will have an accident within the next 3 years?
c. Given that the low-risk driver will have an accident within the next 3 years, what is the probability that the low-risk driver will also have an accident within the next 3 years afterwards (i.e., years 4 through 6)?
d. Give an example of how a low-risk driver and a high-risk driver would NOT be independent. How reasonable is our assumption of independence? Why is the assumption of independence so important for our calculations?

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