An insurance company sells car insurance and flood insurance. Claims come in following a Poisson process with rate 6.

 An insurance company sells car insurance and flood insurance. Claims come in following a Poisson process with rate 6. With probability 2/3 the claim is for car insurance, otherwise it is for flood insurance. Let N(t) be the number of claims that arrive by time t, let N1(t) be the number of car insurance claims that arrive by time t, and let N2(t) be the number of flood insurance claims that arrive by time t. Evaluate the following and show work. a) P(N(t) = 9); b) P(N1(t) = 6); c) P(N2(t) = 3); d) P(N1(t) = 6; N2(t) = 3).