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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).
- Spring '10
- The Land