Probabilities for Total Worth of Binomial Events on Basis of Expected Total Worth

摘要

Many operations research analyses are oriented toward evaluating expected values, but have little or no way of evaluating probability distributions. One situation where knowledge of expected values is essentially equivalent to knowing distributions is that where a distribution is completely determined except for the value of a univariate parameter. Then, evaluating the expected value is nearly always equivalent to evaluating the parameter. This situation occurs for some special cases where independent binomial events are considered and the observed total worth for the outcomes for these events is of interest. Here, a specified amount of worth is associated with each event. This amount occurs, or does not occur. The probability of occurrence is unknown and possibly different for the events. For one of the two cases considered, the events are chosen so that they have the same amount of worth. Then, the distribution of the total worth can often be approximated by use of a binomial distribution with its probability (the only unknown parameter) equal to the arithmetic average of the probabilities for the events. For the second case, the events have known ratios of probabilities. Then, only one unknown parameter occurs. (Author)