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In probability theory, the expected value of a random variable, denoted () or , is a generalization of the weighted average, and is intuitively the arithmetic mean of a large number of independent realizations of The expected value is also known as the expectation, mathematical expectation, mean, average, or first momentExpected value is a key concept in economics, finance, and many other. This is part of a long question im doing I have just come from e^y = e^x c to get to y = ln(e^x c) so dont want to go backwards, (e both sides) I recall (ln) rules are a bit wierd so im sorta stuck I final got y = x ln(c), But i dono if i can ln(e^x c) = ln(e^x) ln(c) Can some1 check this?. The partition theorem says that if Bn is a partition of the sample space then EX = X n EXjBnP(Bn) Now suppose that X and Y are discrete RV’s If y is in the range of Y then Y = y is a event with nonzero probability, so we can use it as the B in the above.

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HOMEWORK 4 SOLUTIONS Exercise 1 Let X, Y be two random variables on (Ω, F, P) Let A⊂F be a subσalgebra The random variables X and Y are said to be independent conditionally on A is for every nonnegative measurable. You can put this solution on YOUR website!. E^x = 271 This article is compiled by Rahul and reviewed by GeeksforGeeks team Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above Attention reader!.

Number e Definition 1 The number e is defined by lne = 1 ie, the unique number at which lnx = 1 Remark Let L(x) = lnx and E(x) = ex for x rational Then L E(x) = lnex = xlne = x, ie, E(x) is the inverse of L(x) ex Inverse of lnx 1 Definition 2 The exp function E(x) = ex is the inverse of the log function. Í Q à Ò % @ * Ñ ' ) J y 4 q À ò ^ Q · ' L & J 6 ® Ú ï ' ) J æ Ú å · ù * * # % v ½ Ä 4 a Ä. G c v y a i k l n f o > @ ` r p t c m h u g?.

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