Stochastic processes #2

On the average, Mr. Z drinks and drives once in 4 years. He knows that

According to the laws of his state, the third time when he is caught drinking and driving results in the loss of his driver's license.

Poisson process is the correct model for such ``rare events'' as drinking and driving.

What is the probability that Mr. Z will keep his driver's license for at least 10 years?

Let the number of times Mr. Z gets pulled over by year

Then is a poisson process with rate

Therefore

Now,



By independent increments,



I've been studying for my stochastic process test on monday (Rock).