V3 9.6 MAXIMUM LIKELIHOOD CRITERION According to this criterion, the decision-maker just selects the state of nature that has the highest probability of occurrence and then picks the decision alternative which will yield the highest payoff in that state of nature. For instance, referring to table 9.26 of example 9.5-4, the icecream retailer would choose the demand level of 17 cups that corresponds to the highest probability of 0.40 and having selected that, would decide in favour of stock action of 17 cups since it results in the largest conditional profit of 51 in that state of nature. This decision criterion produces valid results when the probability of one state of nature is much more than any other and when the conditional values are not too much different This criterion, however, may result in serious errors when a large number of states of nature exist and each of them is associated with a small and nearly equal probability of occurrence. 9.7 EXPECTED VALUE CRITERION FOR CONTINUOUSLY DISTRIBUTED RANDOM VARIABLES The situations considered so far in this chapter involved discrete random variables. Many real situations, however, are concerned with continuously distributed random variables. The expected value criterion discussed earlier can be applied for such situations also. EXAMPLE 9.7-1 A vegetable seller buys tomatoes for 45 a box and sells them for 80 per box. If the box is not sold on the first selling day, it is worth 15 as salvage. The past records indicate that demand is normally distributed, with a mean of 30 boxes daily and a standard deviation of 9 boxes. How many boxes should he stock