Exercise 5-16: A marketing company performed a risk analysisfor a manufacturer o

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Exercise 5-16: A marketing company performed a risk analysisfor a manufacturer of synthetic fibers and concluded that new competitors present norisk 13% of the time (due mostly to the diversity of fibers manufactured), moderaterisk 72% of the time (some overlapping of products), and very high risk (competitormanufactures the exact some products) 15% of the time. It is known that 12international companies are planning to open new facilities for the manufacture ofsynthetic fibers within the next three years. Assume the companies are independent. Let X, Yand Z denote the number of new competitors that will pose no, moderate, andvery high risk for the interested company, respectively. a) What is the range of the joint probability distribution ofX, Y and Z?
Determine the following: b) P (X=1, Y=3, Z=1) c) P (Z 2) d) P (Z=2 | Y=1, X=10) e) P (Z 1 | X=10) f) P (Y 1, Z 1 | X=10) g) E (Z | X=10) Exercise 5-16: A marketing company performed a risk analysisfor a manufacturer of synthetic fibers and concluded that new competitors present norisk 13% of the time (due mostly to the diversity of fibers manufactured), moderaterisk 72% of the time (some overlapping of products), and very high risk (competitormanufactures the exact some products) 15% of the time. It is known that 12international companies are planning to open new facilities for the manufacture ofsynthetic fibers within the next three years. Assume the companies are independent. Let X, Yand Z denote the number of new competitors that will pose no, moderate, andvery high risk for the interested company, respectively. a) What is the range of the joint probability distribution ofX, Y and Z?
Determine the following: b) P (X=1, Y=3, Z=1) c) P (Z 2) d) P (Z=2 | Y=1, X=10) e) P (Z 1 | X=10) f) P (Y 1, Z 1 | X=10) g) E (Z | X=10)

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