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Mean waiting time between accidents

The number of traffic accidents at a certain intersec- tion is thought to be well modeled by a Poisson process with a mean of 3 accidents per year.

a. Find the mean waiting time between accidents.

b. Find the standard deviation of the waiting times between accidents.

c. Find the probability that more than one year elapses between accidents.

d. Find the probability that less than one month elapses between accidents.

e. If no accidents have occurred within the last six months, what is the probability that an accident will occur within the next year?

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## Q : Maximum number of years

An aircraft landing gear has a probability of 10-5 per landing of being damaged from excessive impact. Assuming a landing per day, what is the maximum number of years for which one can give at least a 90% guarantee that the landing gear will stay