Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are -3, 0, 4, 5, and 6. Value x of X P (X = x) -3 0 0.23 5 0.17 6 0.30

A certain reagent is created to test for an infectious disease. The test has anaccuracy rate of p = 90%, and the accuracy does not depend on whether or not thepatient is actually infected. a. If four people are tested for the disease, what is the probability that at leastthree of them receive accurate test results? b. In an area where q = 5% of people are infected, a man’s test result ispositive. What is probability that it is a false positive (which means that he is notinfected but the test is positive due to inaccuracy)?   *please solve for a-b, type or neatly  write your answers on paper, NO EXCEL* thank you !

Senior executives at an oil company are trying to decide whether to drill for oil in a particular field. It costs the company $750,000 to drill. The company estimates that if oil is found the estimated value will be $3,650,000. At present, the company believes that there is a 48% chance that the field actually contains oil.  Before drilling, the company can hire an expert at a cost of $75,000 to perform tests to make a prediction of whether oil is present. Based on a similar test, the probability that the test will predict oil on the field is 0.55. The probability of actually finding oil when oil was predicted is 0.85. The probability of actually finding oil when no oil was predicted is 0.2. What is the EMV if the company hires the expert?

4.1 TYPES OF RANDOM VARIABLES. Which of the following describe continuous random variables? Which describe discrete random variables? The number of newspapers sold by the New York Times each month The amount of ink used in printing a Sunday edition of the New York Times The actual number of ounces in a 1-gallon bottle of laundry detergent The number of defective parts in a shipment of nuts and bolts The number of people collecting unemployment insurance each month

The Cook County Lumber Co. has three sawmills that produce boards of different lengths. The following table is a joint frequency distribution based on a random sample of 1,000 boards selected from the lumber inventory. Board Length Sawmill 8ft 10ft 12ft 14ft A 140 100 80 14 B 250 20 100 50 C 160 50 16 20 Based on these data, if a board is selected that is 12 feet long, the probability that it was made at sawmill A is: 0.20 0.24 0.08 0.41

The University of Miami bookstore stocks textbooks in preparation for sales each semester. It normally relies on departmental forecasts and preregistration records to determine how many copies of a text are needed. Preregistration shows 85 operations management students enrolled, but bookstore manager Vaidy Jayaraman has second thoughts, based on his intuition and some historical evidence. Vaidy believes that the distribution of sales may range from 65 to 85 units, according to the following probability model: Demand Probability 65 0.10 Stock 70 0.30 65 This textbook costs the bookstore $82 and sells for $112. Any unsold copies can be returned to the publisher, less a restocking fee and shipping, for a net refund of $30. a) Based on the given information, Vaidy's conditional profits table for the bookstore is: 65 p=0.10 75 0.20 70 p=0.30 80 0.10 Demand 75 p=0.20 80 p = 0.10 85 p=0.30 85 0.30

An expensive piece of equipment is used in the masking operation for semiconductor manufacture.A capacitor in the equipment fails randomly. The capacitor costs $7.50, but if it burns out while the machine is in use, the production process must be halted. Here the replacement cost is estimated to be $150. Based on past experience, the lifetime distribution of the capacitor is estimated to be                     Number of Months                    Probability of                           of Service                                Failure                                 1                                            .08                                 2                                            .12                                 3                                            .16                                 4                                            .26                                 5                                            .22                                 6…

The company is considering whether or not they should drill the land. The cost of drilling is estimated to be $4 million. The company believes there are three possible findings after drilling the land: dry, wet and gushing. The probabilities for these outcomes are 0.5, 0.3 and 0.2, respectively. If the land is found to be dry, it obviously offers no profit. If the land is wet, it brings a potential profit of $10 million. If gushing, the potential profit from the land is $30 million. Answer the following questions, Q1 and Q2. Q1: Draw a decision tree to show the decision for this company based on the EMV criterion. Nodes and arcs are provided below and you can make more of them by using "copy" and "paste" Q2: The company has the option of using some new technology and equipment combined with seismic survey data to learn the presence of oil (dry, wet or gushing) before drilling the land. However, it requires $2.3 million investment for the technology, equipment, and required analysis. Is…

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