Stochastic

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: 3. We repeated roll two four sided dice with numbers 1, 2, 3, and 4 on them. Let Yk be the sum on the k th roll, Sn = Y1 + · · · + Yn be the total of the first n rolls, and Xn = Sn (mod 6). Find the transition probability for Xn . 1.4. The 1990 census showed that 36% of the households in the District of Columbia were homeowners while the remainder were renters. During the next decade 6% of the homeowners became renters and 12% of the renters became homeowners. What percentage were homeowners in 2000? in 2010? 1.5. Consider a gambler’s ruin chain with N = 4. That is, if 1 i 3, p(i, i + 1) = 0.4, and p(i, i 1) = 0.6, but the endpoints are absorbing states: p(0, 0) = 1 and p(4, 4) = 1 Compute p3 (1, 4) and p3 (1, 0). 1.6. A taxicab driver moves between the airport A and two hotels B and C according to the following rules. If he is at the airport, he will be at one of the two hotels next with equal probability. If at a hotel then he returns to the airport with probability 3/4 and goes to the other hotel with probability 1/4. (a) Find the tran...
View Full Document

This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

Ask a homework question - tutors are online