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Probability distributions are essential to VaR calculations. Take the expected value and variance of the portfolio returns, and apply these to a probability distribution (a portfolio can be thought of as a linear combination of assets, or random variables).

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And so, because there's a finite number of values here, we would call this a discrete random variable. And you can see that this is a valid probability distribution because the combined probability is one. .1 plus 0.15, plus 0.4, plus 0.25, plus 0.1 is one. And none of these are negative probabilities, which wouldn't have made sense.

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All the other boxes should have the value zero (’0’). Percentages. To test for the significance of a difference between an expected and an observed proportion. Input an expected proportion or number in the top box and an observed binomial proportion in the second box. Input a number of cases in the first number of cases box. Averages. To ...

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Means and Variances of Random Variables: The mean of a discrete random variable, X, is its weighted average. Each value of X is weighted by its probability. To find the mean of X, multiply each value of X by its probability, then add all the products. The mean of a random variable X is called the expected value of X.

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Expected Value and Variance 6.1 Expected Value of Discrete Random Variables When a large collection of numbers is assembled, as in a census, we are usually interested not in the individual numbers, but rather in certain descriptive quantities such as the average or the median. In general, the same is true for the probability distribution of a ...

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1 10 = 1 105= 0.00001 (4.2) Therefore, the probability of winning is 0.00001 and the probability of losing is 1 0.00001 = 0.99999 (4.3) The expected value table is as follows. x P(X=x) xP(X=x) Loss -2 0.99999 (-2)(0.99999)=-1.99998 Proﬁt 100,000 0.00001 (100000)(0.00001)=1

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and its cumulative distribution function using the pbvcdf or pbvcdf.2 functions. All functions take three arguments, the rst versions (with no su x) take the three parameters, and the second versions (with a su x) take the expected value of X, the expected value of Y and the covariance between Xand Y.