practicum1 - ISYE 2028 A and B Spring 2009 Practicum 1 Dr....

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Unformatted text preview: ISYE 2028 A and B Spring 2009 Practicum 1 Dr. Kobi Abayomi January 27, 2009 Please be able to show all of own your work and reasoning. Include computer printouts where you can. You won’t need Good Luck. Due Feb. 5th- In class 1 1 Scraps I have invented a dice game. It is called Scraps. It goes like this: A player places a bet, then tosses three 3-sided die 1 , and records the sum of the three die. Play goes like this:-If the sum is 6 on the first toss, the player loses the entire bet and the game is over.-If the sum is 6 on the second toss, the player loses half of her bet and the game is over.-If the sum is 6 on the third toss, the player loses a quarter of her bet and the game is over.-If the sum is 6 on the fourth toss, the player loses nothing; if the sum is not 6 on the fourth toss, the player wins double the initial bet. For an initial bet of one hundred dollars, what are the expected winnings? What is the variance of the winnings? For an initial bet of one thousand dollars, what are the expected winnings? What is variance of the winnings? Fill Fennett goes to Vegas and plays Scraps 1000 times, each time betting 100 dollars. Here is the distribution of his winnings (defined as money he gets back after the each game). Winnings in dollars 50 75 100 200 Total Obs. Frequency 240 180 260 160 160 1000 What is the probability that he would have this outcome, under the assumption i.e. a null hypothesis that he is able to play Scraps fairly? 1 Prisms – where the short faces are plain; each die has 1, 2 and 3 on each long face 2 2 Farmer Njoroge’s Market Njoroge the farmer has a lbs of apples and b lbs of potatoes for sale. The market price, in Kisumu Kenya, for apples each day is a random variable with a mean of μ x dollars and a standard deviation of σ x dollars. Similarly, for a pound of potatoes, the mean price is μ y dollars and the standard deviation is σ y dollars. Assume that the market prices for potatoes and apples has a correlation of ρ . It costs Njoroge d dollars to bring all the apples and potatoes to market. Assume Njoroge will sell all of each type of produce each day. a) Define random variables and use them to express Njoroge’s net income, in terms of the constants a,b,d and the parameters μ x ,μ y ,σ x ,σ y ,ρ . b) Find the mean and the variance of the net income, also in terms of the given constants and parameters. c) Njoroge is a popular name in Kenya. Say, for any Njoroge selling potatoes and apples at the market the correlation, ρ is distributed uniform between .5 and .75. Generate 100 random Njoroges – here ρ is a random quantity — with a = 5 ,b = 10 and 100 more random Njoroges with a =- 5 ,b = 10. Set the means and variances to several values. Generate appropriate plots. Talk about what you see....
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This note was uploaded on 03/22/2009 for the course ISYE 2028 taught by Professor Shim during the Spring '07 term at Georgia Tech.

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practicum1 - ISYE 2028 A and B Spring 2009 Practicum 1 Dr....

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