# Class Notes for 18.44 at Massachusetts Institute of Technology (MIT)

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## 18.44 Lecture Notes - Lecture 13: Mit Opencourseware

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The doob"s optional stopping time theorem is contained in many basic texts on probability and martingales. (see, for example, theorem 10. 10 of. The es

View Document## 18.44 Lecture Notes - Lecture 13: Prati, Ratia, Royal Institute Of Technology

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Break choosing one of the items to be counted into a sequence of stages so that one always has the same number of choices to make at each stage. Then t

View Document## 18.44 Lecture Notes - Lecture 11: Random Variable

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Lecture 11: binomial random variables and repeated trials. Toss fair coin n times. (tosses are independent. ) Can use binomial theorem to show probabil

View Document## 18.44 Lecture Notes - Lecture 10: Dried Lime, Elche, Random Variable

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The variable of x, denoted var(x), is de ned by var(x) = e[(x - ) ] Taking g(x) = (x - ) , and recalling that e[g(x)] = (x - ) p(x), we nd that var[x]

View Document## 18.44 Lecture 1: 18.600 Feb 3, 2016 (Lecture 1)

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Suppose that betting markets place the probability that your favorite presidential candidates will be elected at 58 percent. Price of a contract that p

View Document## 18.44 Lecture Notes - Lecture 22: Internet Message Access Protocol, Independent And Identically Distributed Random Variables, Random Variable

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Say we have independent random variables x and y and we know their density functions f and f. Now let"s try to nd f (a) = p{x + y a} This is the integr

View Document## 18.44 Lecture Notes - Lecture 19: Random Variable, Press Kit, Ert1

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Say x is an exponential random variable of parameter when its probability distribution function is f(x) = For a > 0 we have f (a) = f(x)dx = e dx = - e

View Document## 18.44 Lecture Notes - Lecture 18: Plat

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Let"s plot this for a few values of n. If we replace fair coin with p coin, what"s probability to see k heads. Let"s plot this for p = 2/3 and some val

View Document## 18.44 Lecture Notes - Lecture 30: Light-Year, Winny

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Consider a sequence of random variables x , x , x , . each taking values in the same state space, which for now we take to be a nite set that we label

View Document## 18.44 Lecture Notes - Lecture 16: Random Variable, Public Radio Exchange

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Say x is a continuous random variable if there exists a probability density function f = f on such that. We may assume f(x)dx = f(x)dx = 1 and f is non

View Document## 18.44 Lecture Notes - Lecture 14: Random Variable, Stochastic Process, Philippine Standard Time

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Properties from last time for integer k 0. A poisson random variable x with parameter satis es p{x=k} = The probabilities are approximately those of a

View Document## 18.44 Lecture Notes - Lecture 9: Weighted Arithmetic Mean, Narn, Riak

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Recall: a random variable x is a function from the state space to the real numbers. Can interpret x as a quantity whose value depends on the outcome of

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