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[DOC File]1
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Given a random variable X with cumulative distribution F(x), one can use G to calculate a transformed cumulative distribution function for X equal to G(F(x)). The sorting operation, (9.5.1), described in Step 2 above distinguishes G(X) from the characterization of coherent measures of risk given in the representation theorem (9.5.2) above.
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[DOC File]Chapter 1 Notes
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For the distribution function of Example a, find the cumulative density function. Mean or Expected Value of a Continuous RV (E(X) = (x f(x)dx (Variance/Standard Deviation of a Continuous RV (Var (X) = ((x - E(X))2 f(x)dx ( NORMAL DISTRIBUTIONS. Family of distributions, all with the same general shape. Symmetric about the mean
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[DOC File]California State University, Northridge
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The Excel spreadsheet has a normal distribution function, NORMDIST(x, , , cumulative). In this function x is the value for which the distribution is desired (e.g. a or b in the equations above), and are the parameters in the distribution, and the fourth variable is set to true to give the cumulative distribution.
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[DOC File]The Mathematics of Value-at-Risk
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Building on this idea, the cumulative distribution function of X is defined as follows. Definition 7: Suppose X is a continuous random variable and X(-∞,∞). The . Cumulative Distribution Function of X at a, denoted . F(a), gives the probability that X takes a …
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[DOC File]Chapter 2 : Discrete Random Variables
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3 Cumulative Distribution Function. 4 Expectation, E(X) 5 Expectation of any function of X, E[g(X)] ... Sometimes the probability density function may be expressed as a formula. Example 2.1. Two tetrahedral dice (i.e. 4-faced die), each with faces labeled 1, 2, 3 and 4 are thrown and the score noted, where the score is the sum of the two ...
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Cumulative distribution function general formula