Business Statistics

1
Introduction to Decision Techniques Lesson
1 David Boege 920020 sec 8
2
Questions for this semester?

• Should you rent your home or buy it?
• Should you ask the pretty girl/guy out on a date?
• Should you gamble money on the UNI football game
  this weekend?
• It is Friday night and you have 50 in your
  pocket, what should you do?
• You have 4 different food ingredients in your
  refrigerator, what should you make?
• With gas costs being so high, you want to know
  how to best maximize the fuel economy of your
  car?
• You are training for a marathon and want to keep
  your pulse at 140 bpm, what speed should you run
  at?
• You manufacture tractors and want to know the
  proper amount of tractors to maximize your
  profits?

3
Semester Layout

• Unit 1 Probability, Probability, Probability
• Unit 2 Linear Programming
• Unit 3 Derivatives and Their Applications

4
Unit 1

• Lesson 1 Probability
• What is Probability?
• Three Methods for Assigning Probabilities
• Manipulating Probabilities
• Addition Multiplication Laws
• Bayes Theorem
• Lesson 2 Decision making
• Decision making without probabilities
• Decision making with probability
• Lesson 3 Decision making
• Using Sample Information

5
Probability

• Probability The chance of an event occurring
• Adding all of the Probabilities together always
  1.0
• The Probability of any given event is between 0.0
  and 1.0
• Quantitative versus Qualitative
• Certainty 1.0
• Impossible 0.0
• Likely would be about .75
• Improbable would be about .25
• None are specific values except certainty and
  impossible

6
Probability Methods

• Classical Assigning equal probability to each
  potential outcome
• Relative Frequency Proportion of the total
  frequency that is in any given class interval in
  a frequency distribution
• Subjective Using a persons or groups opinion
  to get give a best guess on the probability

7
Probability

• Experiment Process to produce outcomes that can
  be statistically analyzed
• Event Outcome of an experiment, need one for
  each of the potential experiment outcomes
• Sample Space All of the events that can happen
  in an experiment
• Complement Any event that does not consist of
  the sample points of event A

8
Probabilities Graphically
A
B
9
Unions Intersections

• Union All of the areas that is covered by the
  probabilities of A B
• Intersection The area covered by C below

A
B
C
10
Addition Multiplication Laws

• Addition Law The probability that an event A
  union event B equals the probability of A plus
  the probability of B minus the probability of A
  intersecting B
• P(A B) P(A) P(B) P(A B)
• Multiplication Law The probability that an event
  A occurs given that another event B has occurred
  equals the probability of A intersecting B
  divided by the probability of B
• P(A B) P(A B)
• P(B)

11
Bayes Thereom

• What it does Relates the conditional and
  marginal probabilities of two random events
• Prior/Marginal Probability Does not take into
  account anything about other events
• Conditional Probability Given one event
  occurred, this is the probability of another
  event
• Posterior Probability It is the conditional
  probability that we are trying to determine

12
Bayes Thereom

• Prior/Marginal Probability
• P(A) P(B)
• Conditional Probability
• P(AB) P(BA)
• Posterior Probability
• P(AB)

13
Bayes Thereom

• Question An observer sees a student in this
  class from a distance and can only see that the
  student has a hat on.
• The observer wants to know whether that student
  is a boy or not?
• What do we know about this class?
• Prior/Marginal Probability
• What is the probability that a random student is
  a boy? P(A)
• What is the probability that a random student is
  a girl? (complement A)
• What is the probability that a random student has
  a hat on? P(B)
• What is the probability that a random student
  does not have a hat on? (complement B)
• Conditional Probability
• What is the probability that a boy has a hat on?
  P(BA)
• Posterior Probability
• What is the probability that a student is a boy
  given that they are wearing a hat? P(AB)