Stochastic

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Unformatted text preview: .77 .70 .61 .52 .50 .50 .52 .50 P (H |2M ) .73 .60 .56 .58 .51 .47 .48 .53 .49 P (H |1M ) .71 .60 .52 .58 .51 .56 .47 .51 .46 P (H |1H ) .57 .55 .51 .53 .53 .49 .45 .43 .46 P (H |2H ) .58 .54 .48 .47 .52 .50 .43 .40 .46 P (H |3H ) .51 .59 .36 .53 .48 .48 .27 .34 .32 In fact, the data supports the opposite assertion: after missing a player will hit more frequently. 1.2 Multistep Transition Probabilities The transition probability p(i, j ) = P (Xn+1 = j |Xn = i) gives the probability of going from i to j in one step. Our goal in this section is to compute the probability of going from i to j in m > 1 steps: pm (i, j ) = P (Xn+m = j |Xn = i) As the notation may already suggest, pm will turn out to the be the mth power of the transition matrix, see Theorem 1.1. To warm up, we recall the transition probability of the social mobility chain: 1 2 3 1 .7 .3 .2 2 .2 .5 .4 3 .1 .2 .4 and consider the following concrete question: Q1. Your parents were middle class (state 2). What is the probability t...
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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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