04 STAT probability 4-example IN CLASS REVIEW

04 STAT probability 4-example IN CLASS REVIEW - Dr V.R...

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Dr. V.R. Bencivenga Economics 329 PROBABILITY EXAMPLE FOR REVIEW 1. A large manufacturer is beginning a research project that it hopes will lead to large profits. The research project either will yield a commercial application, or not. If it yields the commercial application, the manufacturer will develop the application. Development of the application will yield a product with two characteristics the product might be better than existing products, or else no better; and the product might be cheaper to produce than existing products, or else more expensive to produce. a. View this process of attempting to discover and take to market a new product as a random trial. What is the sample space ?
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2 1.a. No commercial application Commercial application & development Better and cheaper Better and more expensive No better and cheaper No better and more expensive e 1 e 2 e 3 e 4 e 5
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3 1.a. No commercial application Commercial application & development Better and cheaper Better and more expensive No better and cheaper No better and more expensive e 1 e 2 e 3 e 4 e 5 Better No better Cheaper e 2 e 4 More e 3 e 5 expensive
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4 1.a. No commercial application Commercial application & development Better and cheaper Better and more expensive No better and cheaper No better and more expensive e 1 e 2 e 3 e 4 e 5 Better No better Cheaper e 2 e 4 More e 3 e 5 expensive
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5 1.a. No commercial application Commercial application & development Better and cheaper Better and more expensive No better and cheaper No better and more expensive e 1 e 2 e 3 e 4 e 5
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6 1.a. No commercial application Commercial application & development Better and cheaper Better and more expensive No better and cheaper No better and more expensive e 1 e 2 e 3 e 4 e 5 S = {e 1 , e 2 , e 3 , e 4 , e 5 }
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7 Dr. V.R. Bencivenga Economics 329 PROBABILITY EXAMPLE FOR REVIEW 1. A large manufacturer is beginning a research project that it hopes will lead to large profits. The research project either will yield a commercial application, or not. If it yields the commercial application, the manufacturer will develop the application. Development of the application will yield a product with two characteristics the product might be better than existing products, or else no better; and the product might be cheaper to produce than existing products, or else more expensive to produce. a. View this process of attempting to discover and take to market a new product as a random trial. What is the sample space ? b. The research project will yield a commercial application with probability .6. Development of a commercial application will yield a better product with probability .7, and a cheaper product with .5. “Better/no better” and “cheaper/more expensive” are independent outcomes of the development project. What is the probability distribution over the sample space?
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8 b. Let CA denote “commercial application.” P(e 1 ) = P(no CA) = 1 .6 = .4 No commercial application Commercial application & development e 1 .6 .4
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9 b. Let CA denote “commercial application.” P(e 1 ) = P(no CA) = 1 .6 = .4 No commercial application Commercial application & development e 1 .6 .4
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04 STAT probability 4-example IN CLASS REVIEW - Dr V.R...

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