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20 Dec 2019: Here we describe the concept of quasi-reversibility, provide new examples of quasi-reversible nodes, discuss the range of arrival rates for which a node remains quasi-reversible, and analyse a

17 Jan 2019: Purchasing the rights to a new movie costs £10,000. How muchhave they spent after 5 years? ... Mr. Smithbuys a new car as soon as the old one breaks down or reaches T years.

14 Nov 2019: You may need to read slightly ahead of the lectures to do the questions on theIsing and random-cluster models, but nothing new is needed beyond the requireddefinitions.

14 Feb 2019: Find an injective function h on (0,) such that, writing ψ = h(θ),the maximum likelihood estimator ψ̂ of the new parameter ψ is unbiased.

26 May 2019: Friedman, and R. Tibshirani. TheElements of Statistical Learning. Springer New York, 2001.

10 Nov 2019: A further outstanding question for explicit congestion control is the scale of the step-change in rate that is necessary at a resource to accommodate a new flow.

17 Jan 2019: There are two salesmennear the door who offer passing customers samples of a new product. ... Each customer takesan exponential time of parameter 1 to think about the new product, and during this timeoccupies the full attention of one salesman.

4 Dec 2019: 2E(X)E(X2). > wU′′(w). U ′(w). The new right-hand side wU ′′(w)/U ′(w) is called the Arrow–Pratt coefficient of relativerisk aversion. ... Define a new random process (Yn)n>0 by. Y0 = 0, Yn =nk=1.

14 Mar 2019: It has been a transformative idea. which has led to new unexpected links between a number of probabilistic models and also other.

16 Sep 2019: Probability. About these notes. Many people have written excellent notes for introductorycourses in probability. Mine draw freely on material prepared by others in present-ing this course to students at Cambridge. I wish to acknowledge especially