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Section 14.3 of the text deals with some probability concepts that are essential to the understanding of probability distribution of NPW. As most engineering students take a course in statistics, the material presented in this section should serve primarily as a refresher. The most essential element in this section that you should understand thoroughly is the determination of cumulative probability distribution of a random variable from its probability distribution. We know that random variables can be discrete or continuous. A discrete random variable is one which will take only discrete values. The probability distribution of a discrete random variable is depicted by something similar to bar graphs. The cumulative distribution function derived from such a distribution will be a stepped function. The distribution function of a continuous variable on the other hand will be, as the name signifies, a continuous function. The cumulative distribution function derived from such a distribution will also be a continuous function. The book has examples of a triangular and a uniform distribution function. Both of these distributions are for continuous random variables. Two important measures used to describe random variables are the mean and the variance. The mean is the expected (or the most likely) value of the random variable, while its variance is the expected value of the square of the deviations of all values of the random variable from their mean. The variance provides a measure of variability of the variable. The square root of the variance is the standard deviation of the variable. The last important concept related to probabilities that we will use in our course is related to joint probabilities. A concept related to joint probability distribution is that of conditional probability. A joint probability distribution of a group of random variables is the distribution of group of variables as a whole. We will deal mostly with the joint probability distribution of two random variables. The joint probability distribution of two random variables is the likelihood of observing all combinations of the two variables. Finding the likelihood of each one of all possible combinations of the two variables is easy to observe in the case of discrete random variables. The table shown in the lower part of page 655 is an example of finding all possible combinations of two jointly distributed random variables. Finding the probability distribution of a jointly distributed variable is simplified greatly, if we make the assumption that the two variables are distributed independently. Most examples and problems in the text make this assumption. Conditional probability is not required when we are dealing with joint distribution of independent variables. The joint probability for independently distributed variables is found by multiplying the two probabilities for each variable. Table 14.6 illustrates this principle. |