STAT 400 Lecture AL1 Spring 2015 Dalpiaz More Examples for 2 2 2 3 5 Management of an airline knows that 0 5 of the airline s passengers lose their luggage on domestic flights Management also know that the average value claimed for a lost piece of luggage on domestic flights is 600 The company is considering increasing fares by an appropriate amount to cover expected compensation to passengers who lose their luggage By how much should the airline increase fares 6 A grocer has shelf space for two units of a highly perishable item that must be disposed of at the end of the day if it is not sold Each unit costs 1 70 and sells for 3 50 From past experience the grocer knows that the demand for this item could be either 0 or 1 or 2 units The grocer has to decide whether to stock one unit of this item or two units a Construct the grocer s profit payoff in each of the following cases demand 0 demand 1 demand 2 stock 1 unit stock 2 units b Suppose P demand 0 0 20 P demand 1 0 30 and P demand 2 0 50 Find the expected payoff profit of both actions and choose the optimal action c Suppose P demand 0 0 25 P demand 1 0 30 and P demand 2 0 45 Find the expected payoff profit of both actions and choose the optimal action 7 To save time and money when testing blood samples for the presence of a disease the following procedure is sometimes used Blood samples from a number of people are pooled together and the pooled sample is tested If the pooled sample is negative then no further testing needs to be done If the pooled sample is positive however then each one of the separate samples must be tested individually To be specific suppose that the blood samples of 10 people are pooled together in this procedure and suppose that the proportion of those who have the disease in the population from which the samples are drawn is 0 02 Also assume that the presence of the disease in one sample is independent of the presence of the disease in the other samples a Find the probability that the pooled sample is negative b Let X be the number of tests that must be run Construct the probability distribution of X x c f x Compute the mean of X Is this larger or smaller than 10
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