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Triangular Density Function-ECO6416

Triangular Density Function-ECO6416 - values near the...

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Triangular Density Function The triangular distribution shows the number of successes when you know the minimum, maximum, and most likely values. For example, you could describe the number of intakes seen per week when past intake data show the minimum, maximum, and most likely number of cases seen. It has a continuous probability distribution. The parameters for the triangular distribution are Minimum (a), Maximum (b), and Likeliest (c). There are three conditions underlying triangular distribution: The minimum number of items is fixed. The maximum number of items is fixed. The most likely number of items falls between the minimum and maximum values. These three parameters forming a triangular shaped distribution, which shows that
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Unformatted text preview: values near the minimum and maximum are less apt to occur than those near the most likely value. The following are the general Triangular density function, together with the expected value and the variance for a Triangular random variable X (a, c, b): f(x) = 2(x-a) / [(b-a)(c-a)], for a ≤ x ≤ c f(x) = 2(b-x) / [(b-a)(b-a)], for c ≤ x ≤ b E(X) = (a + b + c) / 3 Var(X) = (a 2 + b 2 + c 2- ab - ac - bc) / 18 The following is a Triangular density function with parameters (a = 0, c = 0.25, a = 1): A Triangular Density Function Application: Given X is distributed as above, compute the tails probability P (X ≤ 0.1 OR X ≥ 0.9)....
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