Question

The traffic incidents in Melbourne and Sydney follow a Poisson process with the rate
of 5 and 6 incidents per hour, respectively.
(a) Find the probability that no traffic accidents will occur in Melbourne in the next
30 minutes.
(b) Find the expected time (in minutes) until 10 new incidents occur in Sydney.
(c) Find the expected time (in minutes) until 10 new incidents in total occur in
Melbourne and Sydney. Hint: For this and the next question, you can assume
that traffic incidents in the two cities are independent.
(d) Assuming exactly 5 traffic incidents in total will occur in Melbourne and Sydney
in the next 10 minutes, find the probability that not more than 2 traffic incidents
will occur in Melbourne during the same period of time. Hint: Use the formula
of conditional probability.

Answer 1