Download Tutorial 7 - WordPress.com

26134 Business Statistics
[email protected]
Tutorial 7: Probability
Key concepts in this tutorial are listed below
1. Construct contingency table
2. Understand Joint events
3. Understand joint probability
4. Understand marginal probability
5. Understand Conditional probability
6. Test of Independence
7. Practically apply the above concepts and calculate
required probabilities
1
Quiz 2 in NEXT WEEK!!!!
The topics to be tested in Quiz 2 are:
THRESHOLD 3: Relating variables and analyzing relationships between
variables.
The specific topics for this threshold are:
1.) Lecture Topic: Simple Linear Regression
2.) Lecture Topic: Multiple Linear Regression
3.) Lecture Topic: Issues with Regression - Specific topics that will be
tested in this lecture are : Use of Dummy Variables in regression
and Multicollinearity.
THRESHOLD 4: Theoretical foundation of statistical inferenceUnderstanding events and using data to calculate the probability of
occurrence of an event.
The specific topics for this threshold are:
1.) Lecture Topic: Probability
The sample quiz will be uploaded one week prior to the quiz.
2
Probability and Events
• Probability (P) is defined as the likelihood (or
chance) that an event (A) will occur.
• Sample Space: is the set of all possible
outcomes of an experiment.
• Event: an outcome of an experiment.
• An event is composed of one or more
elementary events.
3
Complement Events
The complement of any event A is the event that
A does not occur. Both these cannot occur at the
same time. If A denotes the event of rain in
Sydney then A’ denotes the event of no rain in
Sydney.
A’
AA
4
5
6
A={5}
A’={1,2,3,4,6}
Mutually-Exclusive Events
• Occurrence of one event precludes the
occurrence of the other event. Event A and
event B cannot occur at the same time.
P(𝐴∩𝐵)=0
7
• Events A and B are mutually exclusive if when A occurs, B
cannot occur and vice versa. Example of mutually exclusive
events: A – Observing a 1 on the die roll, B – observing a 3 on
the die roll.
8
P(𝐴∩𝐵)=0
Intersection and Union Events
• Intersection (joint event) defined as probability of A
and B occurring at the same time and is denoted as
P(𝐴∩𝐵)
• Union is defined as probability of A or B occurring
denoted a:
P(A U B) = P(A) + P(B) – P(A ∩ B)
9
10
A contingency table is also referred to as the frequency table.
Similarly, probability table is also referred to as the relative frequency table.
11
P(D) = 0.58. This is an example of marginal probability.
NOTE: Row totals or column totals are referred to as marginal probabilities.
NOTE: Mutual exclusive means cannot occur at the same time.
12
Conditional Probability
The conditional probability of A given B is the
joint probability of A and B divided by the
marginal probability of B
P(X|Y)=Joint Event/Marginal Event
P(X  Y)
=
P(Y)
13
NOTE: the key to recognise questions on conditional probability is the word, given.
14
Independent Events
If two events are independent, then their joint
probability is equal to their marginal
probabilities multiplied by each other.
P(X∩Y)=P(X)*P(Y)
15
Summary: Probability





16
Marginal Probability
Union Probability
Joint Probability
Conditional Probability
Independent Probability
@ Dr. Sonika Singh, BSTATS, UTS
U
17
18
19