251x0472 11/22/04 ECO251 QBA1 THIRD EXAMDec 1, 2004 Name: _____________________ Student Number: _____________________ Class Time (Circle) 10am 11am 1pm 2pmPart I: 8 points.z follows the standardized Normal distribution 1,0~ Nz. Find the following. Make diagrams! (0.5 extra credit for each useful diagrams)1. 67.112.2 zP2. 45.167.1 zP3. 45.1zP4. 64.345.1 zP251x0472 11/22/04Part II: (22+ points) Do all the following: All questions are 2 points each except as marked. Exam is normed on 50 points including take-home. (Showing your work can give partial credit on some problems! In open-ended questions it is expected. Please indicate clearly what sections of the problem you are answering and what formulas you are using. Neatness counts!) Remember that you may not be able to finish this section, so ration your time on each problem. [Numbers in brackets are a cumulative total]1. The covariancea) must be between -1 and +1.b) must be positive.c) can be positive or negative.d) must be between zero and +12. The portfolio expected return of two investments a) will be higher when the covariance is zero.b) will be higher when the covariance is negative.c) will be higher when the covariance is positive.d) does not depend on the covariance.3. An average of 16 customers arrive at a checkout counter every minute and we want to find the probability that more than 22 will show in a given minute, the Poisson distribution will be used with a standard deviation of a) 2b) 4c) 16d) here is not enough information.4. (Mansfield) From experience, the director of a computer center knows that any one of the twenty-five PCs in the room is broken 4% of the time. Whether or not any given PC is broken does not depend on how much it is used; they just seem to break down randomly. What type of probability distribution would be used to figure out the probability that more than eight of the PCs will be broken down at the same time?a) binomial distribution.b) Poisson distribution.c) hypergeometric distribution.d) none of the above.5. You receive two tickets for a sold-out concert. You call four potential dates for the evening. You think that there is a chance of 31 that each of the individuals would call back and agree to go to aconcert with you. You will be very embarrassed if more than one accepts. What is the probability that exactly one out of the four says ‘yes?’ (Extra credit: Do this last! What is the probability that you are embarrassed?) Show your work! (3) [11] 2251x0472 11/22/04 Questions 6-10 are based on exhibit 1. Show your work if you expect full credit!Exhibit 1: The table below shows average Fahrenheit temperature and yield in lbs./acre for an industrial crop. F Y 63 10 70 15 . 75 17 79 16 80 20The following calculations are done for you. One more column is needed.Row x 2x y 2y 1 63 3969 10 100 2 70 4900 15 225 3 75 5625 17 289 4 79 6241 16 256 5 80 6400 20 400 367 27135 78 12706. Find the sample standard deviation of Fahrenheit temperatures, x (2)7. Find the sample covariance between Fahrenheit temperature and yield.(3)8. Find the sample correlation between Fahrenheit temperature and yield. (2) [18]9. If the conversion formula for Celsius temperature is C = 5/9(F-32), find the covariance between Celsius temperature and yield. (Hint: You are finding the sample covariance between two random variables, one of which is 916095 xw and the other of which is 01 yv. (2)10. If the conversion formula for Celsius temperature is C = 5/9(F-32), find the correlation between Celsius temperature and yield. (2) [22]3251x0472 11/22/0411. We have twenty units of equipment in a bin of which five are defective. Pull three out at random. What is the probability that exactly one will be defective if we:a. sample without replacement? (3)b. sample with replacement? (2)c. If we sample with replacement, what is he probability that the first item that we find that is defective is the third item that we pick? (2) [29]To get full credit for this problem, identify the distribution that you are using and show your work!12. If ten people are selected at random from a large (continuous) population what is the probability that more than half (which is not exactly six) make more than the median income? To get full credit for this problem, identify the distribution that you are using and showyour work! (2) [31]13. If x is a random variable with a mean of 7 and a standard deviation of 6, finda. 39,48 xxCov (3) b. 39,48 xxCorr (2) [36] 4251x0472 11/22/04 ECO251 QBA1 THIRD EXAMDec 1, 2004TAKE HOME SECTION- Name: _________________________ Student Number: _________________________Throughout this exam show your work! Please indicate clearly what sections of the problem you are answering and what formulas you are using.Part III. Do all the Following (20 Points) Show your work! 1. As everyone knows, a jorcillator has two components, a phillinx and a flubberall. It seems that the jorcillator works as long as one component works. For example, if the Phillinx failed last year and the flubberall fails this year, the phillinx fails this year. This problem, which is a simplified version of Problem H4 has three time periods, last year, this year and Ever After (after this year). You have been in Tibet for the last year, so you have no idea on what actually happened last year.The probability of the phillinx failing is given by a standardized Normal Distribution, so , if zrepresents the life of the Phillinx, the probability of the phillinx failing last year is 0zP, the probability of it failing this year is 10 zP and the probability of it lasting into the Ever After is 1zP. The probability of the Flubberall failing is given by a Continuous Uniform Distribution, where 1c and fd 2, where f is the fourth digit of your student number, divided by 10. For example if Seymour’s student number is 012345, his value of 3.23.2 d. If the fourth digit of your student number is zero, use 1.3d. If xrepresents the life of the Phillinx, the probability of the phillinx failinglast year is 0xP, the probability of it failing this year is 10 xP and the probability of it lasting into the
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