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The key concept used in finding the NPW distribution is the one related to the distribution of a function of a random variable whose distribution is known. Finding the distribution of the function of random variables is simplified when the functional relationship is linear. For example, if we know the distribution of a random variable X, then finding the distribution of a linear function of X is straightforward. This task is simplified further if we are dealing with discrete random variables. Example 14.8 illustrates this process for a jointly distributed variable which is a function of two discrete random variables, X and Y. As seen in Table 14.8, the NPW value for each combination of the two variables, X and Y, are determined, and knowing the distribution of the two variables and with the assumption that X and Y are independent, we can easily find the distribution of the NPW. As the text suggests, ordering the NPW values in increasing magnitude will simplify the task of finding the cumulative distribution of the joint variable, which in this case is the NPW of the project. After the distribution is computed, we can compute the mean and the variance. Decisions about the project can then be made using the expected value of the NPW and the expected variance around the mean. Example 14.9 illustrates how both of these measures, mean and variance, are used in choosing between mutually exclusive projects. |