The number of times that a sample of radioactive material emits particles is modeled by a Poisson process N=(N(t) : t0) with rate >0.

a.)What is the probability that 3 emissions have occurred by time t=2 and 5 emissions have occurred by time t=4?

b.)Conditional on the event that 2 emissions have occurred by time t=1, find the expected value of the time of the first emission.