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Week 5 Lecture Statistics For Decision Making

Week 5 Lecture Statistics For Decision Making. B Heard. Not to be used, posted, etc. without my expressed permission. B Heard. Week 5 Quiz. Your Week 5 Quiz is on material covered in Weeks 3 and 4 Your Week 7 Quiz is on material covered in Weeks 5 and 6

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Week 5 Lecture Statistics For Decision Making

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  1. Week 5 LectureStatistics For Decision Making B Heard Not to be used, posted, etc. without my expressed permission. B Heard

  2. Week 5 Quiz • Your Week 5 Quiz is on material covered in Weeks 3 and 4 • Your Week 7 Quiz is on material covered in Weeks 5 and 6 • Your Final Exam is comprehensive covering the material in the three prior quizzes plus the material covered in Week 7 • Your best approach for preparing for the quizzes should be the Practice Quizzes offered in the previous week (for this week’s quiz the Week 2 Practice Quiz) and the live lecture of the Week the actual Quiz is posted Not to be used, posted, etc. without my expressed permission. B Heard

  3. Week 5 Quiz Let’s look at some questions…. Not to be used, posted, etc. without my expressed permission. B Heard

  4. Week 5 Quiz • How many ways can a committee of 4 be chosen from 20 people? Not to be used, posted, etc. without my expressed permission. B Heard

  5. Week 5 Quiz • How many ways can a committee of 4 be chosen from 20 people? This would be a combination because “order” doesn’t matter, so there would be 4845 different ways. Not to be used, posted, etc. without my expressed permission. B Heard

  6. Week 5 Quiz • How many ways can a committee of 4 be chosen from 20 people if they have distinct positions (i.e. President, Secretary, Treasurer, and Vice-President)? Not to be used, posted, etc. without my expressed permission. B Heard

  7. Week 5 Quiz • How many ways can a committee of 4 be chosen from 20 people if they have distinct positions (i.e. President, Secretary, Treasurer, and Vice-President)? This would be a permutation because “order” does matter, so there would be 116280. Not to be used, posted, etc. without my expressed permission. B Heard

  8. Week 5 Quiz • What values can a probability be? Not to be used, posted, etc. without my expressed permission. B Heard

  9. Week 5 Quiz • What values can a probability be? Anything between 0 and +1 (NOTHING ELSE). That also means from 0% to 100%, and any positive fraction where the numerator is smaller than the denominator. Not to be used, posted, etc. without my expressed permission. B Heard

  10. Week 5 Quiz • Given the following table of College Students by Gender and Major: • Answer the following questions. Not to be used, posted, etc. without my expressed permission. B Heard

  11. Week 5 Quiz What is the probability that a given student is a female? What is the probability that a given student is a Math Major? What is the probability that a given student is male Political Science Major? (This could also be worded “What is the probability that a student is a Political Science Major AND Male) What is the probability that a student is a Business Major given that the student is female? Not to be used, posted, etc. without my expressed permission. B Heard

  12. Week 5 Quiz What is the probability that a given student is a female? 76/150 or .5067 What is the probability that a given student is a Math Major? 10/150 or .0667 What is the probability that a given student is male Political Science Major? (This could also be worded “What is the probability that a student is a Political Science Major AND Male) 20/150 or .1333 What is the probability that a student is a Business Major given that the student is female? 22/76 or .2895 Not to be used, posted, etc. without my expressed permission. B Heard

  13. Week 5 Quiz What is the probability that a student is a Male given that the student is an English Major? What is the probability that a student is female or a Psychology Major? What is the probability that a student is a Business Major or a male? Are being male and being a Business Major independent events? Not to be used, posted, etc. without my expressed permission. B Heard

  14. Week 5 Quiz What is the probability that a student is a Male given that the student is an English Major? 12/25 or .4800 What is the probability that a student is female or a Psychology Major? (76 + 35 – 19)/150 = 92/150 or .6133 What is the probability that a student is a Business Major or a male? (45 + 74 – 23)/150 = 96/150 or .64 Are being male and being a Business Major independent events? If P(male| Business Major) = P(Male) they are independent events. However the probability of being a male student given that they are a business major is 23/25 and the probability of being a male student is 74/150, they are not equal thus these are DEPENDENT events. Not to be used, posted, etc. without my expressed permission. B Heard

  15. Week 5 Quiz • List the sample space of the National League teams in the 2008 MLB playoffs. Not to be used, posted, etc. without my expressed permission. B Heard

  16. Week 5 Quiz List the sample space of the National League teams in the 2008 MLB playoffs. {Brewers, Cubs, Dodgers, Phillies} Not to be used, posted, etc. without my expressed permission. B Heard

  17. Week 5 Quiz What is the probability of drawing a 7 from a deck of cards? And what is the probability of a second card being an Ace or King if the first was a 7? Not to be used, posted, etc. without my expressed permission. B Heard

  18. Week 5 Quiz What is the probability of drawing a 7 from a deck of cards? And what is the probability of a second card being an Ace or King if the first was a 7? What is the probability of drawing a 7 from a deck of cards? 4/52 or 1/13 And what is the probability of a second card being an Ace or King if the first was a 7? There are 8 Aces and Kings left, but only 51 cards to draw from so it would be 8/51 Not to be used, posted, etc. without my expressed permission. B Heard

  19. Week 5 Quiz What is the probability of drawing a 6, 7, or 8 from a deck of cards? What is the probability of a second card drawn being a 6, 7, or 8 if the first was a 6, 8, or 8? Not to be used, posted, etc. without my expressed permission. B Heard

  20. Week 5 Quiz What is the probability of drawing a 6, 7, or 8 from a deck of cards? What is the probability of a second card drawn being a 6, 7, or 8 if the first was a 6, 8, or 8? What is the probability of drawing a 6, 7, or 8 from a deck of cards? There would be 12 of them so 12/52 or 3/13 What is the probability of a second card drawn being a 6, 7, or 8 if the first was a 6, 8, or 8? There would be 11 left and only 51 cards to draw from so it would be 11/51 Not to be used, posted, etc. without my expressed permission. B Heard

  21. Week 5 Quiz • If there are 13 word documents and 27 excel documents in a folder, and one is randomly drawn, what is the probability of drawing a word document? Not to be used, posted, etc. without my expressed permission. B Heard

  22. Week 5 Quiz • If there are 13 word documents and 27 excel documents in a folder, and one is randomly drawn, what is the probability of drawing a word document? 13/ (13+17) = 13/40 Not to be used, posted, etc. without my expressed permission. B Heard

  23. Week 5 Quiz • If the P(A) = 7/20 ; P(B) = 14/20; P(A and B) = 3/20, then what is the P(A OR B)? Are A and B mutually exclusive? Prove your answer. Not to be used, posted, etc. without my expressed permission. B Heard

  24. Week 5 Quiz • If the P(A) = 7/20 ; P(B) = 14/20; P(A and B) = 3/20, then what is the P(A OR B)? Are A and B mutually exclusive? Prove your answer. P(A or B) = P(A) + P(B) – P(A and B) = 7/20 + 14/20 – 3/20 = 18/20 or 9/10 A and B are NOT mutually exclusive because P(A and B) does not equal zero. Not to be used, posted, etc. without my expressed permission. B Heard

  25. Week 5 Quiz ! Factorials Answer the following: 4! 3! * 0! 2! /0! ! ! Not to be used, posted, etc. without my expressed permission. B Heard

  26. Week 5 Quiz Factorials Answer the following: Remember that the factorial sign means x! = x * x-1 * x-2 * … 1, so 4! = 4*3*2*1 = 24 3! * 0! = (3*2*1) * 1 = 6 (remember 0! is ALWAYS = 1) 2! /0! = (2*1)/1 = 2 (remember 0! is ALWAYS = 1) Not to be used, posted, etc. without my expressed permission. B Heard

  27. Week 5 Quiz Decide whether the following experiments would be Binomials, Poissons, or neither.  You test 6 different types of batteries.  The random variable represents the battery that is last longest.  Past experience is that 30% of the time it is the third of the six types. You observe a stop sign for 4 hours.  The random variable represents the number of cars that either completely stopped or didn’t.  Historically 65% of cars come to a complete stop.  A cab company averages three pickups per hour. We're interested in knowing the probability that in a randomly selected hour they will get one pickup.  A company ships computer components in boxes that contain 20 items. We want to know the probability that the 2nd item removed will be defective. Not to be used, posted, etc. without my expressed permission. B Heard

  28. Week 5 Quiz You test 6 different types of batteries.  The random variable represents the battery that is last longest.  Past experience is that 30% of the time it is the third of the six types. Neither, because we are testing 6 different types (it’s not a yes/no, good/bad, two decision type situation) You observe a stop sign for 4 hours.  The random variable represents the number of cars that either completely stopped or didn’t.  Historically 65% of cars come to a complete stop. Binomial, probability given in percentage. For this to be Poisson it would say something like on average 42 cars stop at the stop sign every hour, we want to know the probability of exactly 32 stopping, or more than 45 stopping, etc. – the probability (%) was a tip off that it was binomial  A cab company averages three pickups per hour. We're interested in knowing the probability that in a randomly selected hour they will get one pickup. Poisson, as per the previous question’s answer we are interested in finding out the probability of 1 pickup.  A company ships computer components in boxes that contain 20 items. We want to know the probability that the 2nd item removed will be defective. Neither, we don’t have a probability to start with (Binomial), or an average number of defects (Poisson). Not to be used, posted, etc. without my expressed permission. B Heard

  29. Week 5 Quiz If X = {1, 5, 9, 12} and P(1) = .3, P(5) = .3, P(9) = .2, and P(12) = .2, can we call it a random variable? Not to be used, posted, etc. without my expressed permission. B Heard

  30. Week 5 Quiz If X = {1, 5, 9, 12} and P(1) = .3, P(5) = .3, P(9) = .2, and P(12) = .2, can we call it a random variable? Yes, the sum of the probabilities = (.3+.3+.2+.2) = 1 and they are all between 0 and 1. Not to be used, posted, etc. without my expressed permission. B Heard

  31. Week 5 Quiz Find P(X < 14) for this random variable.  X = {1, 5, 7, 13, 15}.  P(1) = P(5) = P(7) = P(13) = P(15). Not to be used, posted, etc. without my expressed permission. B Heard

  32. Week 5 Quiz Find P(X < 14) for this random variable.  X = {1, 5, 7, 13, 15}.  P(1) = P(5) = P(7) = P(13) = P(15). Since  P(1) = P(5) = P(7) = P(11) = P(13) = P(15) they must add up to 1 therefore the probability for each must be 1/5 since there are five so it is 0.20 then P(x < 14) = P(1) + P(5) + P(7) + P(13) = 0.20 + 0.20 + 0.20 + 0.20 = 0.80 Not to be used, posted, etc. without my expressed permission. B Heard

  33. Week 5 Quiz • If X = {-1, 0, 3, 8} and P(-1) = .3, P(0) = .1, P(3) = .3, and P(8) = .3, can we call it a random variable? Not to be used, posted, etc. without my expressed permission. B Heard

  34. Week 5 Quiz • If X = {-1, 0, 3, 8} and P(-1) = .3, P(0) = .1, P(3) = .3, and P(8) = .3, can we call it a random variable? Do the probabilities add up to one? .3 + .1 + .3 +. 3 = 1 So yes it is (also note that those probabilities have to be between 0 and 1. Not to be used, posted, etc. without my expressed permission. B Heard

  35. Week 5 Quiz • We have a binomial experiment with p = .6 and n = 3.  Set up the probability distribution and compute the mean, variance, and standard deviation. Not to be used, posted, etc. without my expressed permission. B Heard

  36. Week 5 Quiz See Excel Spreadsheet picture that follows. X = {0, 1, 2, 3}P(X = 0) = .0.06 P(X = 1) = .29 P(X = 2) = .43 P(X = 3) = .22E(X) = n*p = 3 * .6 = 1.8 (listed as mean in provided excel spreadsheet picture that follows) V(X) = n*p*q, q = 1 - p = 1 - .6 = .4 V(X) = 3*.6*.4 = .72 (listed as variance in provided excel spreadsheet)standard deviation = sqrt(variance) = sqrt(.72) = .85 (listed as stdev in provided excel spreadsheet picture that follows) Not to be used, posted, etc. without my expressed permission. B Heard

  37. Week 5 Quiz Not to be used, posted, etc. without my expressed permission. B Heard

  38. Week 5 Quiz We have a Poisson with mu = 3. Find P(X = 4), find P(X < 4), find P(X <= 4), compute the mean, variance, and standard deviation.

  39. Week 5 Quiz See Excel Spreadsheet attached to follow on post. P(X = 4) = 0.168 (see picture of excel spreadsheet yellow block)P(X < 4) = 0.647 (see picture of excel spreadsheet green block)P(X <=4) = 0.353 (see picture of excel spreadsheet gray block)mean = variance = 3 (see picture of excel spreadsheet)standard deviation = sqrt(variance) = 1.73 (see picture of excel spreadsheet) Not to be used, posted, etc. without my expressed permission. B Heard

  40. Week 5 Quiz

  41. Week 5 Quiz • We have the random variable X = {5,10} with P(5) = .6 and P(10) = .4. Find E(X). Not to be used, posted, etc. without my expressed permission. B Heard

  42. Week 5 Quiz • We have the random variable X = {5,10} with P(5) = .6 and P(10) = .4. Find E(X). E(X) = sum of (x*P(X)) = 5*P(5) + 10*P(10) = 5*.6 + 10*.4 = 3.0 + 4.0 = 7.0 Not to be used, posted, etc. without my expressed permission. B Heard

  43. Week 5 Quiz Continuous or discrete? • The amount of oil in your car’s engine? • The number of cans of coke in your refrigerator? • Your son’s weight? • The number of cousins you have? • The amount of butter in your butter dish? • The number of classes you have taken and received credit for? Not to be used, posted, etc. without my expressed permission. B Heard

  44. Week 5 Quiz Continuous or discrete? • The amount of oil in your car’s engine? Continuous • The number of cans of coke in your refrigerator? Discrete • Your son’s weight? Continuous • The number of cousins you have? Discrete • The amount of butter in your butter dish? Continuous • The number of classes you have taken and received credit for? Discrete Not to be used, posted, etc. without my expressed permission. B Heard

  45. Week 3 Quiz S STAT CAVE See you next week: “Same Stat Time, Same Stat Channel” Not to be used, posted, etc. without my expressed permission. B Heard

  46. I will post charts at: 4stats.wordpress.com

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