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2010-2 STAT FALL midterm _2 q

# 2010-2 STAT FALL midterm _2 q - Dr V.R Bencivenga Economics...

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1 Dr. V.R. Bencivenga Wednesday Nov. 10, 2010 Economics 329 Fall 2010 MIDTERM EXAM #2 Instructions: Answer the questions below in a blue exam book. Show your work to receive credit . This is an open book, open notes exam. Where applicable, include (i) the sample statistic, (ii) the sampling distribution of the sample statistic, and (iii) the reason why this sampling distribution is valid, based on the assumptions of the question. This information is necessary to receive credit on problems using a sampling distribution of a sample statistic. The exam has ten problems, totaling 130 points. The exam is two hours minutes long. Good luck! (20 points) 1. A small farmer in a developing country grows wheat and cassava. Market prices of wheat and cassava fluctuate from year to year, according to the following joint probability distribution: X = price per bushel of cassava (\$) 2 3 4 5 .2 .05 .05 Y = price per bushel of wheat (\$) 6 .05 .3 .05 7 .05 .05 .2 a. What is the expected price of wheat? The variance of the price of wheat? b. Are the price of cassava and the price of wheat statistically independent? Explain why or why not. c. Give the probability distribution of the price of wheat conditional on a price of 4 for cassava. d. Compute the expected price of wheat conditional on a price of 4 for cassava, and the variance of the price of wheat conditional on a price of 4 for cassava. (15 points) 2. A manufacturing company wants to maintain careful control over the quality of the bolts it uses. Each shipment of bolts, which is very large, is subjected to the following procedure. A random sample of 15 bolts is taken from the shipment, and each is tested for defects. If two or more of the bolts in the sample are found to be defective, the shipment is returned. a. The manufacturer's supplier of bolts guarantees that no more than ten percent of its bolts are defective. If a shipment contains ten percent defectives, what is the expected number of defectives in a sample of 15? b. If a shipment contains ten percent defectives, what is the probability it will be returned? c. Perhaps you think too many shipments are returned, now that you have answered the preceding part.

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2010-2 STAT FALL midterm _2 q - Dr V.R Bencivenga Economics...

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