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Unformatted text preview: station 2. the 4 28 II.4, II.5, II.6 12 A.3/ C 18 IX.1 Introduction to Prob. Mariolys Limit Laws and Comb Marni 3/8 1/4 1/8 Random Structures 20 IX.2 Discrete Limit Laws Sophie a 1/2 1 5.1.18: (a) P 2 = 1/2nd Limit Laws /2 so P is regular. FS: Part C Combinatorial 23 IX.3 Mariolys 1/8 1/4 3/8 (rotating instances of discrete 12 11 presentations) q1 1 (b) The solution space of the system (I − P )x = 0 is t 2 , −∞ < t < ∞ . So if q = q2 is a Quasi-Powers and 13 30 IX.5 Sophie Gaussian limit laws 1 q3 14 Dec 10 Presentations Asst+ 2t + 4 = 1, which is equivalent to t = 1/4. So #3 Due probability vector in this space, we need to have t 1/4 q = 1/2. So after many generations, an offspring has 25% of chances to be AA, 50% of chances to 1/4 be Aa and 25% of chances to be aa. 25 IX.4 5.1.D2: M P = M = 1 1 · · · Continuous Limit Laws Marni 1 5.1.D4: (a) As the steady state vector does not depend of the initial conditions, P k ei converges toward q as kMISHNA, Department of Mathematics, SIMON FRASER UNIVERSITY increases. Dr. Marni Version of: 11-Dec-09 (b) Each column of P k ei converges to q as k increases. 5.2.D2: The first sector must produce the largest dollar amount. C EDRIC C HAUVE , FALL 2013 3...
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