251x0631 4/13/06 ECO251 QBA1 THIRD EXAMVersion 1, Apr 20, 2006 Name: _____________________ Student Number: _____________________ Class Time (Circle) MWF 1, MWF 2, TR 12:30, TR 2.Part I: 16 points.z follows the standardized Normal distribution 1,0~ Nz. Find the following. Make diagrams! 1. 00.211.3 zP2. 02.302.3 zP3. 25.125.1 zPF4. 175.z251x0631 4/13/06x follows the Normal distribution 7,2~ Nx. Find the following. Make diagrams! 5. 00.211.3 xP6. 02.302.3 xP7. 25.125.1 xPF8. 175.x2251x0631 4/13/06Part II: (15+ 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. If x is binomial, and ,20nfind the following (If you substitute another distribution for the binomial, justify it!):a) 93 xP when 40.p. (1.5)b) 1610 xP when 75.p. (1.5)c) 51 xP when 03.p. (2)d) 1xP when 23.p. (2)2. A student calculates that 9353510 FFxP . The student could be working with the a) Binomial Distributionb) Normal distribution.c) Continuous Uniform Distributiond) Exponential distributione) All of the abovef) None of the above. [9]3. If 4.xy , 2.3x, 5.7y, 57 xw and 43 yv, find the following: a) xy (1) b) yx (1.5) c) wv (1.5) d) w (1.5) [14.5]3251x0631 4/13/064. What type of probability distribution will most likely be used to analyze the number of cars with old model radios in the following problem?From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have old model radios installed. The sales manager of one dealership wants topredict the probability out of the 8 new cars it just received that, when each is checked, no more than 2 of the cars have old model radios.a) binomial distribution.b) Poisson distribution.c) hypergeometric distribution.d) none of the above. [16.5]5. The West Nantmeal police department must write, on average, 5 tickets a day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a parameter of 6.5 tickets per day. Interpret the value of the parameter. (1.5)a) The number of tickets that is written most often is 6.5 tickets per day.b) Half of the days have less than 6.5 tickets written and half of the days have more than 6.5tickets written.c) If we sampled all days, the arithmetic average or expected number of tickets written would be 6.5 tickets per day.d) The mean has no interpretation since 6.5 tickets can never be written. [16]6. (Extra credit ) Ben Horim and Levy tell us about a presidential debate in which the sound system failed for a half hour. Assume that the sound system has a failure rate of 1 in 10 hours, which means that the average wait for a failure is 10 hours. Use the exponential distribution. a) What is the probability that the system will fail during a 3-hour event? (1.5)b) What is the probability, that if a back-up system with the same characteristics as the original system is used during the half hour that the original system is down for repairs, itwill fail before the half hour elapses?. (1.5)c) What is the variance of the elapsed time before a failure? (1)4251x0631 4/13/067. Using the joint probability table below, (a) Fill in the missing number (1) (b) check for independence (1), (c) Compute yxCov ,, yxCorr , (4), (d) Compute yxE and yxVar . (2) (e) Find 4 yxP and 04 xyxP(2). 1.01.1.01.01.542420xy [26]5251x0631 4/13/06(Blank page for calculations)6251x0631 4/13/06 ECO251 QBA1 THIRD EXAMApr 25, 2005TAKE 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 (19+ Points) Show your work! Neatness counts!1. Ben Horim and Levy present the following actual returns for stock in Republic Steel and General Foods over a ten year period.Year R1 R2 1 22.5 -23.7 2 9.3 8.6 3 -18.6 4.3 4 48.1 -52.2 5 44.4 62.4 6 56.0 61.4 7 -20.1 9.8 8 -11.0 52.6 9 17.1 17.1 10 22.3 11.7Before you start, personalize the data below as follows. Take the third to last digit of your student number and subtract it from -52.7 in the R2 column. This will make the results for year 4 even more disappointing than they actually were. (Example: Seymour Butz’s student number is 123450. He subtracts the 4 from -52.7 getting -56.7). a) Find the sample mean, variance and coefficient of variation for R2. Use computational formulas. The results must look as if you calculated them by hand, although it is perfectly reasonable to check the results using a computer or a calculator. (2.5)b) Find the sample covariance and correlation between R1 and R2. (3)c) Using a conventional measure of risk, explain which stock is riskier. (1). [6.5] d) Make a table showing 11 portfolios. Start with a portfolio with all your money invested in stock 1 (P1 = 1, P2 = 0), then move to a portfolio with 90% in stock 1 and 10% in stock 2 (P1 = .90, P2 = .10), and move by tenths until you get a portfolio that is all stock 2. (5). The table should look as follows with much wider columns. CsRP01.2.3.4.5.6.7.8.9.11Here R is the weighted average return, s is the standard deviation of the portfolio return, and C is the coefficient of variation.[11.5]7251x0631 4/13/06e) Make a graph . Put the mean return on the y axis and the standard deviation on the x axis. (3) Connect your points in a curve. The C-like curve you will probably get illustrates the tradeoffs between return and risk and is called an investment opportunities frontier. f) Looking at the graph and
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