Unformatted text preview: state 1. Each time, he stays where he is with probability 1/2, and he moves to each one of the other two states with probability 1/4. Let X t be the state of this person at time t , and X = 1. (1) What is the distribution of X 1 , i.e., what is the probability that X 1 = k for k = 1 , 2 , 3? (2) What is the distribution of X 2 ? (3) (Optional) What is the distribution of X 3 ? Problem 3: Suppose at any moment, the probability that there is ﬁre in a classroom is α . If there is a ﬁre, the probability we hear the ﬁre alarm is β . If there is not a ﬁre, the probability that there is ﬁre alarm is γ . Given that we hear the ﬁre alarm, what is the probability that there is ﬁre? 1...
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 Fall '10
 Wu
 Conditional Probability, Probability, Probability theory

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