45 730 Probability & Decision Making (9/15/08)
Topics for todays class: Decision Theory Examples Examples of Binomial and Poisson models
Example: ICI product development
Situation: ICI has developed new (unpatentable) use for anthraquinone (AQ) in paper p
DECISION MAKING
1. A tabular presentation that shows the outcome for each decision alternative under the various states of nature is called: a) a payback period matrix. b) a decision matrix. c) a decision tree. d) a payoff table. 2. The difference between
BASIC PROBABILITY
1. If two events are collectively exhaustive, what is the probability that one or the other occurs? a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given. 2. If two events are collectively exhaustive, what is the probab
45 730 Probability & Decision Making (9/24/08)
Topics for todays class: Continuous Probability Distributions
Exponential Normal
The exponential distribution:
Situation: Examining the length of time until an event occurs
Examples: Time until next arrival
45 730 Probability & Decision Making (10/8/08)
Topics for todays class:
Confidence Intervals
Population Mean Population Proportion
More Simulation Examples
Populations and Samples
A Population is the set of all items or individuals of interest
Exampl
THE NORMAL DISTRIBUTION, OTHER CONTINUOUS DISTRIBUTIONS, AND SAMPLING DISTRIBUTION
1. In its standardized form, the normal distribution a) has a mean of 0 and a standard deviation of 1. b) has a mean of 1 and a variance of 0. c) has an area equal to 0.5.
PROBABILITY AND DECISION MAKING 45-730
QUIZ 2 (OFFLINE)
Problem 1 (Expectation). Consider the following random variables: The random variable X takes the values cfw_0, 1, 2 with equal probabilities. The random variable Y takes the value 9 with probability
PROBABILITY AND DECISION MAKING 45-730
QUIZ 2 (OFFLINE)
Problem 1 (Expectation and Variance). You and your friend play the following game. You toss a six sided dice. Your score, denoted by X, is the number that appears on the dice and your friends score,
PROBABILITY AND DECISION MAKING 45-730
QUIZ 1 (OFFLINE) SOLUTIONS
Problem 1 (Sample Spaces). Four friends toss an unbiased coin each to determine a winner. The person whose coin shows up dierent from all the other three wins. The outcome of any toss is in
Midterm Exam 45-730 Probability Spring 2008
Name
SOLUTION KEY
This test is open notes, open book. Laptops are allowed but Internet communication is strictly forbidden. There are fourteen questions total: ten multiple-choice questions and four problems. F
PROBABILITY AND DECISION MAKING 45-730
REAL QUIZ 3 (OFFLINE)
Problem 1 (pdf and cdf ). Let X be a continuous random variable with pdf f (x) and cdf F (x). 3 Suppose also that f (x) = x for 0 x A and zero everywhere else. 9 a) Find the value of A. b) Compu
Final Exam 45-730 Probability Spring 2008
Name
SOLUTION
This test is open notes, open book. This is an individual work. Communication with anybody except the proctor or
instructor is forbidden.
Laptops are allowed but Internet communication is strictly
45 730 Probability & Decision Making (10/13/08)
Topics for todays class: Review Fill in online evaluations Solve parts of the sample midterm
Overview of Topics
Basic Probability Concepts Discrete Random Variables Decision Theory Continuous Random Variabl
SOME IMPORTANT DISCRETE PROBABILITY DISTRIBUTIONS
1. Thirty-six of the staff of 80 teachers at a local intermediate school are certified in CardioPulmonary Resuscitation (CPR). In 180 days of school, about how many days can we expect that the teacher on b
CONFIDENCE INTERVAL ESTIMATION
1. The width of a confidence interval estimate for a proportion will be a) narrower for 99% confidence than for 95% confidence. b) wider for a sample size of 100 than for a sample size of 50. c) narrower for 90% confidence t
1. A 2. C 3. D 4. C 5. A 6. C 7. D 8. C 9. A 10. B 11. C 12. B 13. C 14. B 15. D 16. A 17. D 18. B 19. B 20. C 21. D 22. C 23. D 24. A 25. B 26. D 27. A 28. C 29. B 30. C 31. B 32. B 33. B
SOLUTIONS TO BASIC PROBABILITY
1. c 2. d 3. d 4. a 5. a 6. c 7. d 8. b 9. d 10. d 11. b 12. d 13. b 14. a 15. c 16. b 17. d 18. a 19. a 20. c 21. b 22. d 23. b 24. b 25. a 26. a 27. b 28. d 29. d 30. b 31. d 32. c 33. a 34. d 35. a 36. c 37. d 38. c 39. c
PROBABILITY AND DECISION MAKING 45-730
QUIZ 1 (OFFLINE) SOLUTIONS
Problem 1 (Sample Spaces and Set Theory). Consider the following random experiment: a (six-sided) die is thrown and a coin is ipped simultaneously. A basic outcome of this experiment is the
PROBABILITY AND DECISION MAKING 45-730
REAL QUIZ 2 (OFFLINE)
Problem 1 (Expectation). Consider the following random variables: The random variable X takes the values cfw_0, 1, 2 with equal probabilities. The random variable Y takes the value 9 with probab
45 730 Probability & Decision Making (9/29/08)
Topics for todays class:
Central Limit Theorem Some continuous distribution problems Implications for Simulation
Preliminaries to a last important result for the normal distribution: Consider n i.i.d. random