Reading Assignments

   Chapter 4: All
   Chapter 5: All except section 5.6
   

Problem Assignments

   Chapter 4: 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 18,
              19, 20, 22, 23, 24, 25, 26, 30, 31, 32, 33, 36, 38, 39, 
              40, 45,48, 54
   Chapter 5: 1, 2, 3, 6, 7, 8, 9, 10, 15, 16, 25, 27, 28, 29, 30, 31, 
              34, 38, 40, 41, 43, 
   

Objectives

I = would be on an open-book Part I of exams
    Part I is handed in before you begin work on the closed-book Part II
* = will definitely be on exam, either Part I or Part II        
	   

Chapter 4: Introduction to Probability

   1. Define probability.
   2. Define, give or recognize examples of, and distinguish between:
	a) an experiment
	b) an outcome
	c) an event
        d) the sample space
        e) a sample point
 * 3. Use proper notation for probabilities.
   4. State the possible range for probabilities.
   5. Explain what is meant by the null event.
   6. State the probability of:
	a) an impossible event
	b) a certain event
   7. State the sum of the probabilities of all events in a sample
        space.
   8. Explain what is meant by a priori classical probability (prior
        probability, classical probability).
   9. Explain what is meant by empirical classical probability 
        (relative frequency probability, posterior probability).
  10. Explain what is meant by subjective probability.
  11. Explain what is meant by the following terms:
	a) simple event
	b) complement of an event
	c) joint event
	d) mutually exclusive events
	e) collectively exhaustive events
	f) independent events
  12. State the law of large numbers.
I*13. Use the counting rules to calculate the number of possible 
        outcomes for processes which produce large numbers of 
        outcomes.
I*14. Use the counting rules to calculate the probability of stated
        events.
 *15. Construct a tree diagram for any given situation and calculate
        the probability of sequences in the diagram, given the 
        probabilities of the component steps.
  16. Interpret a tree diagram for any given situation, including the
        calculation of probabilities of outcomes of sequences.
  17. Draw a Venn diagram from given data.
  18. Interpret a given Venn diagram.
  19. Explain what is meant by
        a) the union of two events
        b) the intersection of two events
        and use proper notation to designate them.
  20. Explain what is meant by conditional probability.
  21. Use proper notation for conditional probability.
I 22. Calculate conditional probabilities.
 *23. Construct a prior probability contingency table from a given
        situation (like a deck of cards).
 *24. Construct a relative frequency probability contingency table
        from given data (by first constructing a prior probability
        contingency table).
 *25. Calculate the probability of a simple, joint, or marginal event 
        using contingency and/or probability tables, either those given 
        to you or those which you create from the raw data.
  26. State the addition rule for P(A or B) for:
	a) events that are mutually exclusive
	b) events that are not mutually exclusive
  27. State the multiplication rule for P(A and B) for:
	a) events that are independent
	b) events that are not independent
 *28. Apply the addition rule and the multiplication rule.
 *29. Perform calculations using Bayes' theorem, given a tree diagram
        and/or a contingency table for the situation (though you could
        also use formulas).

Chapter 5: Discrete Probability Distributions

Discrete Probability Distributions

  30. Define random variable.
  31. Distinguish between discrete random variables and continuous 
        random variables.
  32. State whether discrete random variables are measured or counted.
  33. State whether continuous random variables are measured or 
        counted.
  34. State what kind of numbers (whole or fractional) are allowable 
        for discrete random variables and for continuous random 
        variables.
  35. Give or recognize examples of discrete and continuous variables.
  36. State whether probability distributions represent samples of 
        populations.
  37. Use proper notation for probability distributions and their
        characteristics.
  38. Construct discrete probability distributions from theoretical (a 
        priori) outcomes or from empirical outcomes.
  39. Give a bar graph for any given discrete probability distribution.
I 40. Calculate the mean/expected value of a discrete probability 
        distribution.
  41. Explain why the expected value of a discrete probability 
        distribution may not be literally meaningful.
I 42. Calculate the variance and standard deviation of a discrete 
        probability distribution.

Binomial Probability Distributions

 *43. State the assumptions for the binomial distribution with regard 
        to:
	a) number and kind of trials
	b) possible outcomes
	c) relationship of one trial to other trials
	d) the variability of the probability of success throughout the
           trials
 *44. State the following properties for the binomial distribution:
	a) what is meant by a success
	b) possible values of the number of successes
	c) the relationship between infinite or finite populations and
           whether selection is done with replacement or without
  45. Give or recognize examples of binomial experiments.
  46. State whether the binomial probability distribution changes shape 
        for different combinations of n and p.
  47. State the relationship between symmetry or skewness of the 
        binomial distribution and the value of p.
  48. State the correlation between the size of n and the skewness of 
        the binomial probability distribution.
  49. Create a tree diagram for a binomial experiment.
  50. Calculate probabilities from a tree diagram for a binomial 
        experiment.
I 51. Calculate binomial probabilities using the binomial probability 
        function.
 *52. Use binomial probability tables to approximate single or 
        cumulative binomial probabilities.
  53. State what the sum of the probabilities in any column in a 
        binomial table must be for a given value of n. 
I 54. Calculate the mean of a binomial probability distribution.
I 55. Calculate the variance and standard deviation of a binomial 
        probability distribution.

Poisson Probability Distributions

 *56. Describe the Poisson distribution with regard to:
	a) number of trials
	b) frequency of events described
	c) the possible range of occurrences in an interval
	d) the variability of the expected number of occurrences in 
           an interval throughout an experiment
 	e) how intervals can be measured
	f) typical values of average occurrences
  57. Give or recognize some examples of Poisson-distributed phenomena.
  58. Explain what µ refers to in Poisson distributions.
  59. State 
	a) whether the value of µ is typically a whole number
	b) whether µ can often be observed in practice
I 60. Calculate Poisson probabilities using the Poisson probability 
        function. 
I 61. Calculate the mean, variance, and standard deviation of a Poisson
        distribution.
  62. State the relationship between the size of µ and the symmetry or
        skewness of the Poisson distribution.
 *63. Use Poisson probability tables to approximate probabilities.
  64. State what the sum of the probabilities in any column in a 
        Poisson table must be for a given value of µ.