## Probability Distributions for Project Managers

If we plot the probability (density) function (PDF) on a graph with vertical axis as probability and horizontal axis as value of X, then that plot is called a "distribution." The PDF is aptly named because the PDF shows the distribution of value according to the probability that that value will occur, as illustrated in Figure 2-3. [9] Although the exact numerical values may change from one plot to the next, the general patterns of various plots are recognizable and have well-defined attributes. To these patterns we give names: Normal distribution, BETA distribution, Triangular distribution, Uniform distribution, and many others. The attributes also have names, such as mean, variance, standard distribution, etc. These attributes are also known as statistics.

0.0 0.\$ 1-0 1.5 2.0 2-5 3.0 Normalized random variable value

The lotal area under a probability dislribulion curve must be equal to t.O. Therefore, the probability axis is scaled to achieve the requirement of area = 1.0

Finding the area is mathematically a malter o! inlegfaling the function lhat describes the curve, or summing e piece-wise set of rectangles that are arbitrarily small in widlh so Ihal Ihe area ouiside the curve is minimized-Figure 2-3: Probability Distribution.