STAT 333 finalreview_withanswers

STAT 333 finalreview_withanswers - Final Exam Review 1....

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 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) [1] the average number of taxis waiting, and (b) [1/2] the proportion of arriving customers that get taxis. 2. Assume { X n } n is a Markov chain with t.p.m. . 3 0 . 2 0 . 5 . 3 . 5 0 . 2 . 4 0 . 6 . 3 0 . 7 (a) Find the two step transition probability matrix. . 09 0 . 38 0 . 53 . 09 0 . 32 0 . 59 . 34 0 . 66 . 33 0 . 67 (b) [(0, 0.45, 0.325, 0.63)] Suppose that the probability function of X 1 is given by the vector (0 , . 5 , , . 5) . Find the probability function of X 3 . (c) [ { , 1 } , Transient; { 2 , 3 } , Recurrent and Aperiodic] Classify the state space. For each class, determine whether it is recurrent or transient. Determine their periods. (d) [Two Classes implies that MC is reducible] What does it mean by irreducible? Is this MC reducible? (e) [ = 0 , 2 = 1 / 3 ] Find the long run proportions of times when the MC is in state 0, in state 2. (f) [8/3] 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) [mean = 1050, variance = 30000] 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?...
View Full Document

Page1 / 4

STAT 333 finalreview_withanswers - Final Exam Review 1....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online