# Stochastic

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

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