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ANALYSIS II—EXAMPLES 4 Mich. 2014 The questions marked with ...
https://www.dpmms.cam.ac.uk/study/IB/AnalysisII/2014-2015/14sheet4revised.pdf27 Feb 2015: Nj=1 ‖γ(tj) γ(tj1)‖ where the sup is taken over all. finite partitions 0 = t0 < t1 <. < tN = 1. (i) Give an example for which (γ) =. If γ is continuously -
41 Paper 1, Section I 7H StatisticsSuppose that X1, ...
www.statslab.cam.ac.uk/~rrw1/stats/StatisticsTriposQuestions.pdf17 Sep 2015: for j 6= i. Prove that the random vectors Yj AjX are independent, and thatY (Y T1 ,. , Y TJ )T has a multivariate normal distribution.[ Hint: Random vectors are independent if -
21 Paper 4, Section I 9H Markov ChainsLet X0, ...
www.statslab.cam.ac.uk/~rrw1/markov/MarkovChainTriposQuestions.pdf17 Sep 2015: Assume p > q. Let Tj = inf{n > 1 : Xn = j} if this is finite, and Tj = otherwise. ... Let Ti = inf{n > 1 : Xn = i}. For each i 6= j letqij = P(Tj < Ti | X0 = i) and mij = E(Tj | X0 = i). -
19 Paper 2, Section I 3F ProbabilityLet U be ...
www.statslab.cam.ac.uk/~rrw1/prob/ProbabilityTriposQuestions.pdf17 Sep 2015: Find the probability-generating functions of the random variables Hj and Tj. -
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https://www.lib.cam.ac.uk/files/thistgeog_2.pdf20 May 2015: RF4&' #!F,',15(00& #$F,''lZ& #RF,')(/5 #WUFn-&;V' #OFn-&);1c,'; #$F'&1)& #RJ5194(m #WJ&1.Q%l2'&) #RJ,';,7+& #TJ,16) #OJ'nC& #WG1'& #IG1'&jS,(' #!K(()-l'& #
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