In this chapter, we will introduce some basic concepts in statistics. This simplifies statistical inference in practice. This curvature change will show up as an inflection on the cumulative probability curve. If pi = 1/n, where "n" is the number of values in the summation, then E(X) is mathematically equal to the calculation of arithmetic average. For our purposes, integration is nothing more than summation with arbitrarily small separation between values. For instance, we can define a random variable Z = X + Y, or W = X2. 3. Two... 1. There we see two tasks, Task 1 and Task 2, with a finish-to-start precedence between them. The median is the value that is half the distance between the absolute value of the most pessimistic value and the most optimistic value. Can we predict the outcome of toss 101 or know with any certainty whether the outcome of toss 101 will be heads or tails, 10 days duration or 15? There are only 3 black marbles left and only 11 marbles in the jar. Many things can go wrong that are drivers on the pessimistic estimate; usually, there are fewer things that could go right. We may not know at the outset of a project if a regulation will be passed or a contract option exercised, but we can calculate the probability that an action will occur, yes or no. [4]A Guide to the Project Management Body of Knowledge (PMBOK Guide) — 2000 Edition, Project Management Institute, Newtown Square, PA, chap. Lifetime ranges of tools, facilities, and components are generally thought of as continuous. In the questionnaire the enterprises are asked to breakdown their turnover by a number of products, services and client categories. Many physical and tangible objects in projects fit this description. Random variables can be discrete or continuous over a range. Statistics is intimately linked to probability theory. The fields of statistics and probability use numerical data to analyze information and assess the likelihood of possible outcomes of an event. To do this, you throw the die a great number of times and record the outcomes. Why so? The entire structure of probability, and therefore of statistics, can be built on the relatively straightforward foundation given in this chapter. Well, you use probability theory to calculate the probability that your result occurred by chance — if this probability is very small, then you should conclude that the Prime Minister is popular. This textbook covers probability theory and statistical theory in a coherent framework that will be useful in graduate studies in economics, statistics and related fields. In this chapter, we will introduce some fundamental estimation methods for distributional model parameters. Once these estimates are made, then an analysis can be done of the expected value and variance of each random variable, the cost variable, and schedule duration variable. © Copyright 2003-2020 So far, we have discussed random events (tails coming up on a coin toss) and probability spaces (a coin toss can only be heads or tails because there is nothing else in the probability space), but we have not formally talked about the numerical value of an event. Recall that the cumulative probability accumulates from 0 to 1 regardless of the actual distribution being summed or integrated. There is a lot more to know about conditional probabilities because they are very useful to the project manager in decision making and planning. The difference arises from the fact that in the original program developed at Motorola, the mean of the distribution was allowed to "wander" 1.5σ from the expected mean of the distribution. [1] Uncertainty is present in every project, every project being a unique assembly of resources and scope. The probability function [7] is the mathematical relationship between a random variable's value and the probability of obtaining that value.

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