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UCLA STATS 100A - WINTER2014-PMIDTERM1-KEY

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Stat 100 -Intro ProbabilityPractice midterm 1-Multiple choice partJ. SanchezUCLA Department of StatisticsDO NOT DETACH ANY PAGES FROM THIS EXAM. EXAM MUST STAY STAPLED DURING THE WHOLEEXAM TIME.UCLA ID: − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − −− YOUR ID MUST BE WRITTENON THE SCANTRON AND MUST BE ON THE TABLE DURING THE EXAM. YOU MUST WRITE ID ON ALL PAGESOF EXAM.LAST NAME (Please, PRINT): − − − − − − − − − − − − − − − − − − −− FIRST NAME: − − − − − − − − −− YOUR NAMEMUST BE WRITTEN ON THE SCANTRON. CHEAT SHEET MUST HAVE YOUR NAME ON BOTH SIDES. YOUMUST WRITE NAME ON ALL PAGES OF THE EXAM.Instructions• Reading the instructions posted in the Midterm 1 folder in CCLE is required. Students not complying will lose points inthe exam.• ID must be ready to show at all times during the exam. NO ID, no exam.• Close the tables on your left and right. You may not use the empty seats next to you to put things.• The scantron requires number 2 pencil. If you do not have a number 2 pencil raise your hand and one will be given toyou.• Only scientific calculator, one side of a 8 × 11 cheat sheet (according to instructions given in CCLE midterm 1 folder),number 2 pencil, pen, exam and scantron can be on your desk. Everything else (disconnected) in your backpack and yourbackpack on the floor.• YOU MUST HAVE DISCONNECTED YOUR PHONE BEFORE ENTERING the exam and can not turn it on until youleave the room. The same with computers. You can not talk to each other while in the room, you can not exchange papersor information, and you can not use your phone or other electronic devices. All your things must be on the floor in frontof you. Your exam grade will be lower otherwise. You may not keep your phone in your pockets. Put on professor‘stable if you do not have a back pack.• Honor code and student code of conduct applies.• Cheat sheet can have only formulas and definitions, no solved problems, no examples of any kind, no proofs, no numericalexamples, no intermediate steps and no drawings or graphs of any kind. YOUR NAME MUST BE ON CHEAT SHEETAT ALL TIMES. Be ready to show your cheat sheet when the instructor requests it. The cheat sheet must be written allin English. Cheat sheets that do not comply will result in lower grade in the exam.• Failure to follow instructions given here will result in loss of points in the exam at first warning.The exam containsWinter, 2014 1Stat 100 -Intro ProbabilityPractice midterm 1-Multiple choice partJ. SanchezUCLA Department of Statistics• Cover page (write your name and ID)• Multiple choice questions. Answers must be marked on exam and the scantron with your name and ID. Work is notrequired and will not be read.• A couple or three problems to show work. Not shown here. Examples are examples given in lecture, done in TA sessionor in homework. REview those.• Scratch paper (do not detach. Work in scratch paper will not be read).Winter, 2014 2Stat 100 -Intro ProbabilityPractice midterm 1-Multiple choice partJ. SanchezUCLA Department of StatisticsMULTIPLE CHOICE QUESTIONS. ONLY ONE ANSWER IS CORRECT. CHOICE MUST BE MARKED ON THESCANTRON, AND ALSO HERE ON THE EXAM. ONLY THE SCANTRON WILL BE GRADED. NO MARKS ONSCANTRON OR MORE THAN ONE MARK WILL RESULT IN 0 POINTS FOR THE QUESTION NOT MARKED,EVEN IF IT IS MARKED ON THE EXAM. SCRATCH WORK CAN BE DONE NEAR THE MULTIPLE CHOICEQUESTIONS BUT IT WILL NOT BE GRADED.IF YOU DO NOT FIND THE CORRECT ANSWER AMONG THE ONES GIVEN, SELECT THE CLOSEST ANDWRITE YOUR REASONING NEAR THE QUESTION.Problem 1. If the outcome of an experiment is the order of finish in a race among 7 horses having post positions 1,2,3,4,5,6,7,then how many outcomes are there in the sample space? Mark your answer here and in the scantron.(a) 823543(b) 15000(c) 35(d) 5040(e) 34000Solution 1. S, the sample space, consists of all 7! = 5040 permutations of (1,2,3,4,5,6,7) or 5040. For example, one possibleoutcome is (2,3,1,6,5,4,7) which means that the number 2 horse comes in first, the number 3 horse comes second, and so on.Problem 2. Suppose a foreman must select one worker from a pool of four available workers (numbered 1, 2, 3, 4) for a specialjob. He selects the worker by mixing the four names and randomly selecting one. Let A denote the event that worker 1 or 2 isselected, let B denote the event that worker 1 or 3 is selected, and let C denote the event that worker 1 is selected. One of thefollowing is true; which one? Mark your answer here and in the scantron.(a) A and B are not independent(b) A and C are independent(c) A and C are not independent(d) The probability of event AB is 3/4(e) The probability of event BC is 1/2Solution 2. Randomly selected means that the probability of selecting each of the workers is 1/4 .P(A)=P(1 or 2) = 1/4 + 1/4 = 1/2P(B)=P(1 or 3) = 1/4 +1/4 = 1/2P( C) = 1/4; P(AB)=P(1)= 1/4Are A and B independent? Yes, 1/4 = P(AB)=P(A)P(B) = 1/4A and C are not independent: P(AC) = P(1)=1/4 , P(A)P(C)= 1/2 x 1/4 = 1/8Problem 3. A series of 3 jobs arrive at a computing centre with 3 processors. Assume that each of the jobs is equally likelyto go through any of the processors. Find the probability that all processors are occupied. Mark your answer here and in thescantron.(a) 2/9(b) 5/9Winter, 2014 3Stat 100 -Intro ProbabilityPractice midterm 1-Multiple choice partJ. SanchezUCLA Department of Statistics(c) 1/3(d) 4/7(e) 5/4Solution 3. Answer: 2/9Why?For all 3 processors to be busy when 3 jobs arrive, there must be one job in each processor. Thus the probability is(3!)/33= 2/9Problem 4. Consider a plant manufacturing chips of which 10% are expected to be defective. A sample of 5 chips is randomlyselected, and the number of defectives X is observed. The probability of obtaining at most 2 (2 or less) defectives is (Mark youranswer here and in the scantron).(a) 0.057(b) 0.1(c) 0.5(d) 0.001(e) 0.991Solution 4. Answer: 0.991 Why?P(X < 3 | n = 5, p = 0.1) =500.10(0.9)5+510.1(0.9)4+520.12(0.9)3= 0.991Problem 5. Let S = (0, 1] and define Ai= ((1/i), 1], i = 1, 2, ...... Which of the following is NOT true? Mark your answerhere and in the scantron.(a) The events Aii = 1, 2, .... do not form a partition of the sample space(b)S∞i=1Ai= (0, 1](c) The events are not mutually exclusive(d) The union of these events is the sample space.(e)T∞i=1Ai=


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UCLA STATS 100A - WINTER2014-PMIDTERM1-KEY

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