# probability spinner 10 001

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## Introduction to Probability - Chapter 10 pptx

... 2 0 0 0 10 Z8 3 0 0 0 13 Z9 2 0 12 0 0 16 Z10 0 12 0 0 17 Z11 0 13 0 0 15 Z12 6 0 15 0 0 18 Proﬁt -5 0 250 -1 00 50 250 -1 00 300 -5 0 -1 00 -5 0 750 -5 0 -5 0 200 -5 0 -5 0 -5 0 50 850 -5 0 Table 10. 4: Simulation ... 11 0 0 0 12 0 Z10 0 0 0 10 0 0 0 14 0 Z11 0 0 0 16 0 0 0 13 0 Z12 0 0 0 25 0 0 0 10 0 Proﬁt 200 -5 0 -5 0 -5 0 -1 00 300 -5 0 1300 -1 00 -5 0 -1 00 50 -5 0 550 100 -5 0 -5 0 Table 10. 5: Simulation of chain ... CHAPTER 10 GENERATING FUNCTIONS 2.5 1.5 0.5 10 15 20 25 Figure 10. 4: Simulation of Zn /mn for the Keyﬁtz example the sum of 100 0 independent experiments we can use the Central Limit Theorem to...
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## Introduction to Probability phần 10 doc

... same ﬁxed probability vector w 14 If P is a reversible Markov chain, is it necessarily true that the mean time to go from state i to state j is equal to the mean time to go from state j to state ... are the ﬁxed probability row vector for P Then the matrix I−P+W has an inverse Proof Let x be a column vector such that (I − P + W)x = To prove the proposition, it is suﬃcient to show that x ... 0  9 /10 −1/20 3/20 =  −1 /10 6/5 −1 /10  , 3/20 −1/20 9 /10 so  Z = (I − P + W)−1 86/75 =  2/25 −14/75 2/5 1/5 2/5  1/25 −14/75 21/25 2/25  1/25 86/75 Using the Fundamental Matrix to Calculate...
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