Multiple choice questions. I need answers and explanations!
The next 10 questions refer to a variable x distributed as follows: x l 2 Wm Prob(x) . l .2 1. The value ofkis a) .3 b) .5 c) .3" d) indeterminate 2. The expected value of x is a) 2.0 b) 2.1 c) 2.6 d) indeterminate 3. The expected value of x squared is a) 4.0 b) 6.76 c) 7.2 d) indeterminate 4. The variance of xis a) 0.44 b) 0.66 c) 4.6 d) indeterminate 5. If all the x values were increased by 5 in this table. then the answer to question 2 would be a) unchanged b) increased by 5 c) multiplied by 5 d) indeterminate 6. If all the x values were increased by S in this table, then the answer to question 3 would be a) unchanged b) increased by 25 c) multiplied by 25 d) none of the above 7. If all the x values were increased by 5 in this table, then the answer to question 4 would be a) unchanged b) increased by 25 c) multiplied by 25 d) none of the above 8. If all the x values were multiplied by 5 in this table. then the answer to question 2 would be b) unchanged b) increased by 5 c) multiplied by 5 d) indeterminate 9. If all the x values were multiplied by 5 in this table. then the answer to question 3 would be b) unchanged b) increased by 25 c) multiplied by 25 d) none of the above 10. If all the x values were multiplied by 5 in this table. then the answer to question 4 would be a) unchanged b) increased by 25 c) multiplied by 25 d) none of the above The next 1? questions refer to variables X and Y with the following joint distribution PTOMXX) 11. The value ofk is a) 0 b) .l c) .2 d) indeterminate 12. If I know that Y=4, then the probability that X=3 is a) .1 b) .25 c) .4 d) .6 13. If I don't know anything about the value of Y, then the probability that X=3 is a) .1 b) .2 c) .4 d) .6 13. If 1 don't know anything about the value of Y. then the probability that X=3 is a) .1 b) .2 c) .4 d) .6 14. If 1 know that Y=5. then the expected value of X is a) 0.55 b) 2.0 c) 2.2 d) 2.5 15. If 1 don't know anything about Y, then the expected value of x is a) 2.0 b) 2.25 c) 2.45 d) indeterminate 16. If 1 know that Y=5, then the variance of X is a) 17. a) .56 b).1r'5 c)4.84 d) 5.4 If I don't know anything about Y, then the variance of x is .55 b) .14 c} 6.0 d) 6.55 18. The covariance between X and Y is a) 0.0 bl .09 c} .19 d) .29 19. The correlation between X and Y is a) 20. a) 21. a) 22. a) 23. a) 24. a) 25. a) 26. a) 27. a] 28. 0.0 bl .29 c} .4? d) .54 If all the X values in the table above were increased by 8, then the answer to questii 18 would be unchanged b) increased by 8 c) multiplied by 8 d) multiplied by 64 If all the X values in the table above were increased by 8, then the answer to questii 19 would be unchanged b) increased by 8 c) multiplied by 8 d) multiplied by 64 If all the X values and all the Y values in the table above were increased by 8. then the answer to question 18 would be unchanged b) increased by 8 c) multiplied by 8 d) multiplied by 64 If all the X values and all the Y values in the table above were increased by 8. then the answer to question 19 would be unchanged b) increased by 8 c) multiplied by 8 d) multiplied by 64 If all the X values in the table above were multiplied by 8, then the answer to questi 18 would be unchanged b) increased by 8 c) multiplied by 8 d) multiplied by 64 If all the X values in the table above were multiplied by 8, then the answer to questi 19 would be unchanged b) increased by 8 c) multiplied by 8 d) multiplied by 64 If all the X values and all the Y values in the table above were multiplied by 81 then the answer to question 18 would be unchanged b) increased by 8 c) multiplied by 8 d) multiplied by 64 If all the X values and all the Y values in the table above were multiplied by 81 then the answer to question 19 would be unchanged b] increased by 8 c) multiplied by 8 d) multiplied by 64 The distribution of X when Y is known is called the distribution of X, an is written as . These blanks are best lled with a] conditional, 1500 b] conditional, p(X |YJ c] marginal. p(X) d) marginal, p(X IYJ me answer [0 question 15" WDlllcl DC a) unchanged b) increased by 8 c) multiplied by B d) multiplied by 64 28. The distribution of X when Y is known is called the distribution of X. ar. is written as . These blanks are best lled with a] conditional, p(X) b) conditional, p(X IY) c] marginal. p(X) d) marginal, p(X IY) 29. The distribution of X when Y is not known is called the distribution of )i and is written as . These blanks are best lled with a) conditional, 1300 b) conditional, p(X |Y) c) marginal, p(X) d) marginal, p(X |Y) The next 5 questions refer to the following information. You have estimated the equati: wage = alphahat + betahat*experience to predict a person's wage using years of experience as an explanatory variable. Your results are that alphahat is 5.0 with standai error 0.8, betahat is 1.2 with standard error 0.1, and the estimated covariance between alphahat and betahat is 0.005. What this means is that 5.0 is a realization of a random variable with unknown mean and standard error 1.0, and 1.2 is a realization of another random variable which has unknown mean and standard error 0.01. 30. The estimated variance of your forecast of the wage of a person with no experience a) 0.64 b) 0.8 c) 0.81 (1) none ofthese 31. The estimated variance of your forecast of the wage of a person with one year of experience is a) 0.01 b) 0.64 c) 0.65 d) none of these 32. The estimated variance of your forecast of the wage of a person with two years of experience is a) 0.64 b) 0.65 c) 0.66 d) 0.6? 33. The estimate of the increase in wage enjoyed by a person with three additional year of experience is a) 3.6 b) 8.6 c) 15 (1) none of these 34. The estimated variance of the estimate of the increase in wage enjoyed by a person with three additional years of experience is a) 0.01 b) 0.03 c) 0.09 d) none of these The next 9 questions refer to the following information. The percentage returns from stocks A, B, and C are random variables with means 0.05. 0.08, and 0.12 respectively, and variances 0.04, 0.09. and 0.16, respectively. The covariance between A and B retu1 is minus 0.0]; the return from stock C is independent of the other two. A GIC is availal with a guaranteed return of 0.03. 35. If you buy a thousand dollars each of A and B, your expected percentage return for this portfolio is a) 0.05 b) 0.065 C) 0.08 d) none of these 36. If you buy a thousand dollars each of A and B, the variance of your percentage retl for this portfolio is a) 0.11 b) 0.12 c) 0.13 d) none ofthese
