lec_mc

lec_mc - Example: Baseball ! A member of the Little League...

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1 1 Example: Baseball ! A member of the Little League baseball team can be a substitute, a starter or a star. Find the steady state distribution for the transition matrix given below. 0.6 0.3 0.1 Star 0.4 0.5 0.1 Starter 0.3 0.5 0.2 Subst Star Starter Subst 2 Baseball continued … ! What is the average number of seasons it would take to transition from a starter to a star?
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2 3 Mean First Passage Times ! m ij = E(# steps from i until j is reached) ! Note that: + = j k kj ik ij m p m 1 i ii m π 1 = 4 Revisiting the Cola Example ! What is the average number of purchases before a Cola1 customer switches to Cola2? Photo from http://www.angelfire.com/oh/cocacolaantiques/
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3 5 The Geometric Distribution ! A discrete random variable X follows a geometric distribution if: 2 1 1 ) ( ; 1 ) ( , 2 , 1 , 1 0 where , ) 1 ( ) | ( p p X Var p X E x p p p p x X P x = = = = = " 6 Back to Baseball Example ! Suppose there is one more state, that of quitting the team: 1 0 0 0 Quit 0.1 0.6 0.2 0.1 Star 0.1 0.4 0.4 0.1 Starter 0.2 0.2 0.4 0.2 Subst Quit Star Starter Subst
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4 7 Absorbing Chain ! s = number of states ! m = number of absorbing states ! s – m = number of transient states
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lec_mc - Example: Baseball ! A member of the Little League...

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