DR SUSANNE HANSEN SARAL
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DR SUSANNE HANSEN SARAL
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Conditional Probabilities Statistical Independence. Week 6 (1) презентация
Содержание
- 1. Conditional Probabilities Statistical Independence. Week 6 (1)
- 2. Interpreting probability No matter what method
- 6. Two events occur
- 7. The
- 11. Conditional Probability
- 13. Conditional Probability
- 14. Conditional Probability
- 15. Conditional Probability
- 16. Conditional Probability
- 17. Conditional Probability A conditional probability is the
- 18. Conditional Probability -
- 19. Conditional
- 20. Conditional Probability Example DR SUSANNE HANSEN SARAL,
- 21. Conditional Probability – manufacturing example DR SUSANNE HANSEN SARAL, SUSANNEHANSENSARAL@GMAIL.COM
- 22. Conditional Probability - example DR SUSANNE HANSEN SARAL, SUSANNEHANSENSARAL@GMAIL.COM
- 23. Conditional Probability - example DR SUSANNE HANSEN SARAL, SUSANNEHANSENSARAL@GMAIL.COM
- 24. Conditional Probability - example DR SUSANNE HANSEN SARAL, SUSANNEHANSENSARAL@GMAIL.COM
- 25. Class exercises Discrimination in the workplace
- 26. Class exercises What is the probability
- 27. Class exercises (continued) DR SUSANNE HANSEN SARAL, SUSANNEHANSENSARAL@GMAIL.COM
- 28. Statistical Independence
- 29. Statistical independence
- 30. Statistical Independence
- 32. DR SUSANNE HANSEN SARAL, SUSANNEHANSENSARAL@GMAIL.COM
Слайд 1BBA182 Applied Statistics Week 6 (1) Conditional Probabilities
Statistical Independence
Слайд 2 Interpreting probability
No matter what method is used to assign probabilities, we
interpret the probability, using the relative frequency approach for an infinite number of trails.
The probability is only an estimate (Turkish: tahmin), because the relative frequency approach defines probability as the “long-run” relative frequency.
The larger the number of observations the better the estimate will become.
Ex.: Tossing a coin
Head and tail will only occur 50 % in the long run
Computer simulations
The probability is only an estimate (Turkish: tahmin), because the relative frequency approach defines probability as the “long-run” relative frequency.
The larger the number of observations the better the estimate will become.
Ex.: Tossing a coin
Head and tail will only occur 50 % in the long run
Computer simulations
DR SUSANNE HANSEN SARAL
Слайд 5 Definition of marginal probability
Represent
the totals found in the margins of a contingency table:
Marginal probabilities
Marginal probabilities
Слайд 7
The following contingency table shows opinion
about global warming among U.S. adults, broken down by political party affiliation.
DR SUSANNE HANSEN SARAL
Слайд 8
A) What is the probability that a U.S. adult selected at random believes that global warming is a serious problem?
B) What type of probability did you find in part A? (marginal or joint probability)
C) What is the probability that a U.S. adult selected at random is a Republican and believes that global warming is a serious issue?
D) What type of probability did you find in part C? (marginal or joint probability)
DR SUSANNE HANSEN SARAL
Слайд 10 Conditional Probability
What if
we were given the information that the selected person is a republican, instead of U.S. adult? Would that change the probability that the selected person’s opinion about global warming is a nonissue?
Слайд 12 Conditional
Probability
When we restrict our focus to republicans, we look only at the republican’s row of the table,
Which gives the conditional probability of opinion on Global warming “given” the person is republican.
Слайд 17 Conditional Probability
A conditional probability is the probability of one event, given
that another event has already occurred:
DR SUSANNE HANSEN SARAL, SUSANNEHANSENSARAL@GMAIL.COM
The conditional probability of A given that B has occurred
The conditional probability of B given that A has occurred
Слайд 18 Conditional Probability - Example
What
is the probability that a car has a CD player, given that it has AC ?
i.e., we want to find P(CD | AC)
i.e., we want to find P(CD | AC)
DR SUSANNE HANSEN SARAL, SUSANNEHANSENSARAL@GMAIL.COM
Of the cars in a second hand car dealer’s shop, 70% have air conditioning (AC) and 40% have a CD player (CD). 20% of the cars have both.
Слайд 19 Conditional Probability Example
DR SUSANNE HANSEN
SARAL, SUSANNEHANSENSARAL@GMAIL.COM
No CD
CD
Total
AC
.2
.5
.7
No AC
.2
.1
.3
Total
.4
.6
1.0
Of the cars on a used car lot, 70% have air conditioning (AC) and 40% have a CD player (CD).
20% of the cars have both.
Слайд 20 Conditional Probability Example
DR SUSANNE HANSEN SARAL, SUSANNEHANSENSARAL@GMAIL.COM
No CD
CD
Total
AC
.2
.5
.7
No AC
.2
.1
.3
Total
.4
.6
1.0
Given AC, we
only consider the top row (70% of the cars). Of these, 20% have a CD player.
(continued)
Слайд 21 Conditional Probability – manufacturing example
DR SUSANNE HANSEN SARAL, SUSANNEHANSENSARAL@GMAIL.COM
Слайд 25 Class exercises
Discrimination in the workplace is illegal and companies that do
so are often sued. The female professors at a large university recently sued the university, about the last round of promotions from assistant professor to associate professor:
An analysis of the relationship between gender and promotion produced the following probabilities:
An analysis of the relationship between gender and promotion produced the following probabilities:
DR SUSANNE HANSEN SARAL, SUSANNEHANSENSARAL@GMAIL.COM
Слайд 26 Class exercises
What is the probability of promotion given female assistant professors
?
What is the probability of promotion given male assistant professors?
Is it reasonable to accuse the university of gender difference?
What is the probability of promotion given male assistant professors?
Is it reasonable to accuse the university of gender difference?
DR SUSANNE HANSEN SARAL, SUSANNEHANSENSARAL@GMAIL.COM
Слайд 28 Statistical Independence
Two events are statistically independent
if and only if:
Events A and B are independent when the probability of one event is not affected by the other event
If A and B are independent, then
Events A and B are independent when the probability of one event is not affected by the other event
If A and B are independent, then
DR SUSANNE HANSEN SARAL, SUSANNEHANSENSARAL@GMAIL.COM
if P(B)>0
if P(A)>0
Слайд 30 Statistical Independence
Car example
DR SUSANNE HANSEN
SARAL, SUSANNEHANSENSARAL@GMAIL.COM
No CD
CD
Total
AC
.2
.5
.7
No AC
.2
.1
.3
Total
.4
.6
1.0
(continued)
So the two events are not statistically independent
Слайд 31
Class exercise Independent-dependent events
Determine whether the event A3 and B2 are independent or dependent events. P(A3|B2) = P(A3)?
Determine whether the events B1 and A1 are independent or dependent events. P(A1|B1) =P(A1)?
DR SUSANNE HANSEN SARAL, SUSANNEHANSENSARAL@GMAIL.COM
