The payoff matrix for a game is given by 1 −4 −4 2. Compute the expected payoffs of the game for the pairs of strategies in parts (a–d). (Round your answers to one decimal place.) (a) P = 1 0 , Q = 1 0 E = (b) P = 0 1 , Q =
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The payoff matrix for a game is given by
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1 | −4 |
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−4 | 2 |
Compute the expected payoffs of the game for the pairs of strategies in parts (a–d). (Round your answers to one decimal place.)
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1 | 0 |
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1 |
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0 |
E =
(b)
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0 | 1 |
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1 |
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0 |
E =
(c)
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E =
(d)
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0.6 | 0.4 |
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0.1 |
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0.9 |
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- Redo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of Kenyan beans, and 150 grams of French roast beans and the gourmet blend contains 100 grams of Colombian beans, 350 grams of Kenyan beans, and 50 grams of French roast beans. This time the merchant has on hand 30 kilograms of Colombian beans, 15 kilograms of Kenyan beans, and 15 kilograms of French roast beans. Suppose one bag of the house blend produces a profit of $0.50, one bag of the special blend produces a profit of $1.50, and one bag of the gourmet blend produces a profit of $2.00. How many bags of each type should the merchant prepare if he wants to use up all of the beans and maximize his profit? What is the maximum profit?Q1: Who is more likely to feel vulnerable after being a victim of a vialent crime? We hypothesize that blacks are more likely to feel ANGER than whites Feel anger Yes Row Total Race No White A в (fo) 237 (fe). Row% (fo) 602 (fe). Row% (fo) 839 100% Black D E F (fo) 29 (fe). Row% (fo) 123 (fe) Row% (fo) 152 100% Column G Total (fo) 266 (fo) 725 (fo) 991 STEP 1. Do this calculation What did you get? Write the result in the blue box in the cell marked with the letter (C*G/ (C* H)/ (F* G)/ (F* H)/ STEP 2. A B D Cell OBSERVED EXPECTED OBSERVED FREQUENCY SQUARE NOW DIVIDE THE NUMBER IN FREQUENCY (THE NUMBER FREQUENCY (THE NUMBER IN THE BLUE BOX IN THE CELL MINUS EXPECTED THE NUMBER THE PREVIOUS IN THE PREVIOUS EXPECTED FREQUENCY IN THE CELL) COLUMN BY THE COLUMN FREQUENCY FOR THAT CELL (THE BLUE BOX NUMBER) A D E TO GET YOUR CHI-SQUARE, ADD ALL THE NUMBERS IN THE LAST COLUMN >Let x1 and x2 be the payoffs of two investment
- An agricultural field trial compares the yield of two varieties of corn. The researchers divide in half each of 8 fields of land in different locations and plant each corn variety in one half of each plot. After harvest, the yields are compared in bushels per acre at each location. The 8 differences (Variety A - Variety B) give ī = 3.28 and s = 2.14. Does this sample provide evidence that Variety A had a higher yield than Variety B? (a) State the null and alternative hypotheses: (Type "mu" for the symbol u , e.g. mu >1 for the mean is greater than 1, mu <1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1) Ho : 0 Ha : 0 (b) Find the test statistic, t = (C) Answer the question: Does this sample provide evidence that Variety A had a higher yield than Variety B? (Use a 5% level of significance) (Type: Yes or No)y = (1+ va) (3 – 2) %3D 3 -3x+; 2 2 x3 3 11 5 3 5 2 2 11 5 -3x - - 3 O Option 2 Option 1 3 -3x 352 2 x2 +x3 11 5 11 5 3x- Option 4 O option 3An agricultural field trial compares the yield of two varieties of corn. The researchers divide in half each of 17 fields of land in different locations and plant each corn variety in one half of each plot. After harvest, the yields are compared in bushels per acre at each location. The 17 differences (Variety A - Variety B) give a = 2.81 and s = 2.85. Does this sample provide evidence that Variety A had a higher yield than Variety B? (a) State the null and alternative hypotheses: (Type "mu" for the symbol u , e.g. mu > 1 for the mean is greater than 1, mu < 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1) Но : На : (b) Find the standardized test statistic, t = (c) Answer the question: Does this sample provide evidence that Variety A had a higher yield than Variety B? (Use a 5% level of significance) (Type: Yes or No)
- An investment club has set a goal of earning 15% on the money it invests in stocks. The members are considering purchasing three possible stocks, with their cost per share (in dollars) and their projected growth per share (in dollars) summarized in the following table. (Let x = computer shares, y = utility shares, and z = retail shares.) Stocks Computer (x) Utility (y) Retail (z) Cost/share 30 44 26 Growth/share 6.00 6.00 2.40 (c) What is the minimum number of shares of computer stock they should buy? What is the number of shares of the other stocks in this case? utility shares retail sharesAn investment club has set a goal of earning 15% on the money it invests in stocks. The members are considering purchasing three possible stocks, with their cost per share (in dollars) and their projected growth per share (in dollars) summarized in the following table. (Let x = computer shares, y = utility shares, and z = retail shares.) Stocks Computer (x) Utility (y) Retail (z) Cost/share 30 44 26 Growth/share 6.00 6.00 2.40 (a) If they have $392,000 to invest, how many shares of each stock should they buy to meet their goal? (If there are infinitely many solutions, express your answers in terms of z as in Example 3.)An investment club has set a goal of earning 15% on the money it invests in stocks. The members are considering purchasing three possible stocks, with their cost per share (in dollars) and their projected growth per share (in dollars) summarized in the following table. (Let x = computer shares, y = utility shares, and z = retail shares.) Stocks Computer (x) Utility (y) Retail (z) Cost/share 30 44 26 Growth/share 6.00 6.00 2.40 (a) If they have $392,000 to invest, how many shares of each stock should they buy to meet their goal? (If there are infinitely many solutions, express your answers in terms of z as in Example 3.) (х, у, z) %3D (b) If they buy 900 shares of retail stock, how many shares of the other stocks should they buy? computer shares utility shares What if they buy 1800 shares of retail stock? computer shares utility shares (c) What is the minimum number of shares of computer stock they should buy? shares What is the number of shares of the other stocks in this case? utility…
- An investment club has set a goal of earning 15% on the money it invests in stocks. The members are considering purchasing three possible stocks, with their cost per share (in dollars) and their projected growth per share (in dollars) summarized in the following table. (Let x = computer shares, y = utility shares, and z = retail shares.) Stocks Computer (x) Utility (y) Retail (z) Cost/share 30 44 26 Growth/share 6.00 6.00 2.40 (x, y, z) = (a) If they have $392,000 to invest, how many shares of each stock should they buy to meet their goal? (If there are infinitely many solutions, express your answers in terms of z as in Example 3.) (b) If they buy 500 shares of retail stock, how many shares of the other stocks should they buy? What if they buy 1000 shares of retail stock? (c) What is the minimum number of shares of computer stock they should buy? sharesWhat is the number of shares of the other stocks in this case? (d) What is the maximum number of shares of…6. Vx -2+1%= Vx – 2 %3DThe boxplots for the grade scores in the midterm exam in a Calculus I class for two different classes is attachedClass 1: Q1= 65 M= 70 Q3 = 80Class 2: Q1= 60 M= 70 Q3 = 75Which class is likely to have a greater percentage of students with grades smaller or equal to 70? Class 2 Class 1 It is impossible to tell. Neither Both classes are about equal. Which class has 50% percentage of students with grades between 70 and 80? Class 2 Both classes are about equal. Neither It is impossible to tell. Class 1 For which class did 25% of students receive grades between 60 and 70? Both classes are about equal. Class 1 Class 2 Neither It is impossible to tell.