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ECO 329 Examples

ECO 329 Examples - DESCRIPTIVE STATISTICS Dr V.R Bencivenga...

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1 DESCRIPTIVE STATISTICS Dr. V.R. Bencivenga Economic Statistics Economics 329 2010-11 DESCRIPTIVE STATISTICS PART 2 LINEAR TRANSFORMATIONS EXAMPLE

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2 DESCRIPTIVE STATISTICS Linear transformations Begin with two variables, X and Y. Take the linear transformations W = a + b X and Z = c + d Y. X b a W Y d c Z 2 X 2 2 W S b S 2 Y 2 2 Z S d S S WZ = bd S XY otherwise r 0 d , b or 0 d , b if r r XY XY WZ
3 DESCRIPTIVE STATISTICS A pizza restaurant’s monthly pizza sales are X pizzas. Costs of materials are \$2 per pizza, and the price charged by the restaurant is \$12 per pizza. The restaurant pays 10% of its month revenue to the owner of the pizza franchise. Also, the restaurant pays \$5000 in rent and insurance, and \$3000 in labor costs. a. Give the restaurant’s monthly profit (Y) as a function of pizza sales. Y = (.9)(12 2) X 8000 => Y = 8000 + 9 X b. Average monthly sales are 1500 pizzas. The variance of monthly sales is 100 (squared pizzas). What is average monthly profit? What is the variance of monthly profit?

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