University of the Philippines – Diliman
Department of Industrial Engineering and Operations Research
IE 143 Long Quiz 2
Long Quiz 2 Review Problems
1.
Three white and three black balls are distributed in two urns in such a way that each contains three balls. At
each step, we draw one ball from each urn and place the ball drawn from the first urn into the second, and
conversely with the ball from the second urn. Construct the transition probability matrix if we say that the
system is in state i, i = 0, 1, 2, 3 if the first urn contains i white balls. (++)
2.
Suppose that if it has rained for all of the past three days, then it will rain today with probability 0.8; if it
did not rain for any of the past three days, then it will rain today with probability 0.2; and in any other case
the weather today will, with probability 0.6, be the same as the weather yesterday. Construct the transition
probability matrix for this Markov chain. (++)
3.
Suppose that coin 1 has probability 0.7 of coming up heads, and coin 2 has probability 0.6 of coming up
heads. If the coin flipped today comes up heads, then we select coin 1 to flip tomorrow, and if it comes up
tails, then we select coin 2 to flip tomorrow. If the coin initially flipped is equally likely to be coin 1 or coin
2, then what is the probability that the coin flipped on the third day after the initial flip is coin 1? (+)
4.
Suppose in problem 3 that the coin flipped on Monday comes up heads. What is the probability that the
coin flipped on Friday of the same week also comes up heads? (+)
5.
On any given day Gary is cheerful (
C
), soso (
S
), or glum (
G
). If he is cheerful today, then he will be
C
,
S
,
or
G
tomorrow with respective probabilities 0.5, 0.4, 0.1. If he is feeling soso today, then he will be
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.
 Spring '11
 a
 Operations Research, Probability, Markov chain, Andrey Markov, Gary

Click to edit the document details