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Probability Functions
Jun 04,2008 00:00
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Probability FunctionsRandom variables do not have deterministic values. In advance of a random outcome, like the uncertain duration or cost of a work package, the project team can only estimate the probable values, but the team will not know for sure what value is taken until the outcome occurs. Of course, we do not know for sure that the event will happen at all. The event itself can only be predicted probabilistically. In the coin toss, the probability of any specific value of H or T happens to be the same: H = 1 or 0 on any specific toss, 1 if heads, else 0, and similarly for T. p(H = T = 50 in toss of 100) = 0.5 But equal values may not be the case for all random variables in all situations. p(D = 7 in one roll of two die) = 1/6 = 0.167 p(D = 5 in one roll of two die) = 1/9 = 0.111 where D = value of the sum of the two faces of the die on a single roll. The probability function [7] is the mathematical relationship between a random variable's value and the probability of obtaining that value. In effect, the probability function creates a functional relationship between a probability and an event: f(X | value) = p(X = some condition or value) f(X | a) = p(X = a), where the "|" is the symbol used to mean "evaluated at" or "given a value of the number "a". Example: f(H | true) = 0.5 from the coin toss. |