{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

STAT 333 finalreview

# STAT 333 finalreview - Final Exam Review 1 Consider a taxi...

This preview shows pages 1–2. Sign up to view the full content.

Final Exam Review 1. Consider a taxi station where taxis and customers arrive in Poisson processes with respective rates of one and two per minute. A taxi will wait no matter how many other taxis are present. However, if an arriving customer does not find a taxi awaiting, she leaves. Find: (a) the average number of taxis waiting, and (b) the proportion of arriving customers that get taxis. 2. Assume { X n } n 0 is a Markov chain with t.p.m. 0 0 . 3 0 . 2 0 . 5 0 . 3 0 0 . 5 0 . 2 0 0 0 . 4 0 . 6 0 0 0 . 3 0 . 7 (a) Find the two step transition probability matrix. (b) Suppose that the probability function of X 1 is given by the vector (0 , 0 . 5 , 0 , 0 . 5) . Find the probability function of X 3 . (c) Classify the state space. For each class, determine whether it is recurrent or transient. Determine their periods. (d) What does it mean by ”irreducible”? Is this MC reducible? (e) Find the long run proportions of times when the MC is in state 0, in state 2. (f) Calculate lim n →∞ E ( X n ) . 3. The number of claims received at an insurance company during a week is a random variable with mean 20 and variance 120. The amount paid in each claim is a random variable with mean 350 and variance 10000. Assume that the amounts of different claims are independent. (a) Suppose this company received exactly 3 claims in a particular week. The amount of each claim is still random as already specified. What are the mean and variance of the total amount paid to these 3 claims in this week?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern