At a service station they arrive with two types A and B of jobs. Arrivals of each type are a Poisson process with parame

[answerhappygod]

At a service station they arrive with two types A and B of jobs.
Arrivals of each type are a Poisson process with parameter λA = 4
and λB = 5, respectively. Type A jobs take exactly one minute to be
fixed, type B jobs take exactly 2 minutes. The service station
started operating quite some time ago.
1. Find the expected value, variance, and probability function of
the total (both A and B) failures arriving at the station in a time
interval of 3 minutes.
2. We know that in a given 10-minute interval, exactly 6 jobs have
arrived. What is the probability that exactly 3 of these were of
type A?
3. At t = 0 there are no jobs at the service station. What is the
probability function of the number of type A jobs before a type B
job arrives?
4. At t = 0, there are exactly two jobs of type A being served.
What is the probability density probability density of the time at
which the last (before time 0) job of type A arrived?