🗊Презентация Conditional Probabilities Statistical Independence. Week 6 (1)

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Conditional Probabilities Statistical Independence. Week 6 (1), слайд №1Conditional Probabilities Statistical Independence. Week 6 (1), слайд №2Conditional Probabilities Statistical Independence. Week 6 (1), слайд №3Conditional Probabilities Statistical Independence. Week 6 (1), слайд №4Conditional Probabilities Statistical Independence. Week 6 (1), слайд №5Conditional Probabilities Statistical Independence. Week 6 (1), слайд №6Conditional Probabilities Statistical Independence. Week 6 (1), слайд №7Conditional Probabilities Statistical Independence. Week 6 (1), слайд №8Conditional Probabilities Statistical Independence. Week 6 (1), слайд №9Conditional Probabilities Statistical Independence. Week 6 (1), слайд №10Conditional Probabilities Statistical Independence. Week 6 (1), слайд №11Conditional Probabilities Statistical Independence. Week 6 (1), слайд №12Conditional Probabilities Statistical Independence. Week 6 (1), слайд №13Conditional Probabilities Statistical Independence. Week 6 (1), слайд №14Conditional Probabilities Statistical Independence. Week 6 (1), слайд №15Conditional Probabilities Statistical Independence. Week 6 (1), слайд №16Conditional Probabilities Statistical Independence. Week 6 (1), слайд №17Conditional Probabilities Statistical Independence. Week 6 (1), слайд №18Conditional Probabilities Statistical Independence. Week 6 (1), слайд №19Conditional Probabilities Statistical Independence. Week 6 (1), слайд №20Conditional Probabilities Statistical Independence. Week 6 (1), слайд №21Conditional Probabilities Statistical Independence. Week 6 (1), слайд №22Conditional Probabilities Statistical Independence. Week 6 (1), слайд №23Conditional Probabilities Statistical Independence. Week 6 (1), слайд №24Conditional Probabilities Statistical Independence. Week 6 (1), слайд №25Conditional Probabilities Statistical Independence. Week 6 (1), слайд №26Conditional Probabilities Statistical Independence. Week 6 (1), слайд №27Conditional Probabilities Statistical Independence. Week 6 (1), слайд №28Conditional Probabilities Statistical Independence. Week 6 (1), слайд №29Conditional Probabilities Statistical Independence. Week 6 (1), слайд №30Conditional Probabilities Statistical Independence. Week 6 (1), слайд №31Conditional Probabilities Statistical Independence. Week 6 (1), слайд №32
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BBA182 Applied Statistics Week 6 (1) Conditional Probabilities Statistical Independence Dr Susanne Hansen Saral Email: susanne.saral@okan.edu.tr https://piazza.com/class/ixrj5mmox1u2t8?cid=4# www.khanacademy.org
Описание слайда:
BBA182 Applied Statistics Week 6 (1) Conditional Probabilities Statistical Independence Dr Susanne Hansen Saral Email: susanne.saral@okan.edu.tr https://piazza.com/class/ixrj5mmox1u2t8?cid=4# www.khanacademy.org

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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
Описание слайда:
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

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Conditional Probabilities Statistical Independence. Week 6 (1), слайд №3
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Conditional Probabilities Statistical Independence. Week 6 (1), слайд №4
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Definition of marginal probability Represent the totals found in the margins of a contingency table: Marginal probabilities
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Definition of marginal probability Represent the totals found in the margins of a contingency table: Marginal probabilities

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Definition of joint events (AB) Two events occur together : Joint probabilities
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Definition of joint events (AB) Two events occur together : Joint probabilities

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The following contingency table shows opinion about global warming among U.S. adults, broken down by political party affiliation.
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The following contingency table shows opinion about global warming among U.S. adults, broken down by political party affiliation.

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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)
Описание слайда:
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)

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A) What is the probability that a U.S. adult selected at random believes that global warming is a serious problem? = = 63 % B) What type of probability did you find in part A? (marginal or joint probability) Marginal 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? = = 18 % D) What type of probability did you find in part C? Joint probability
Описание слайда:
A) What is the probability that a U.S. adult selected at random believes that global warming is a serious problem? = = 63 % B) What type of probability did you find in part A? (marginal or joint probability) Marginal 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? = = 18 % D) What type of probability did you find in part C? Joint probability

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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?
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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?

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Conditional Probability
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Conditional Probability

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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.
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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.

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Conditional Probability Of the 500 republicans, 290 of them say that global warming is not an issue. We write the probability that a random selected persons believes that global warming is not an issue “given” the person is republican: P(nonissuerepublican) = = 0.58 or 58 %
Описание слайда:
Conditional Probability Of the 500 republicans, 290 of them say that global warming is not an issue. We write the probability that a random selected persons believes that global warming is not an issue “given” the person is republican: P(nonissuerepublican) = = 0.58 or 58 %

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Conditional Probability If we now focus on democratic instead. Of the 500 democratic people only 85 say that global warming is a nonissue: We write the probability that a random selected persons believes that global warming is not an issue “given” the person is democratic: P(nonissuedemocratic) = = 0.17 or 17 %
Описание слайда:
Conditional Probability If we now focus on democratic instead. Of the 500 democratic people only 85 say that global warming is a nonissue: We write the probability that a random selected persons believes that global warming is not an issue “given” the person is democratic: P(nonissuedemocratic) = = 0.17 or 17 %

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Conditional Probability If we focus on “serious concern”: Of the 755 people who say that global warming is a serious concern 415 are democratic We write the probability that a random selected person is democratic “given” the person is says global warming is a serious concern: P(democratic serious concern) = = 0.549 or 55%
Описание слайда:
Conditional Probability If we focus on “serious concern”: Of the 755 people who say that global warming is a serious concern 415 are democratic We write the probability that a random selected person is democratic “given” the person is says global warming is a serious concern: P(democratic serious concern) = = 0.549 or 55%

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Conditional Probability P(nonissue |republican) = = = .58
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Conditional Probability P(nonissue |republican) = = = .58

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Conditional Probability A conditional probability is the probability of one event, given that another event has already occurred:
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Conditional Probability A conditional probability is the probability of one event, given that another event has already occurred:

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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)
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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)

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Conditional Probability Example
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Conditional Probability Example

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Conditional Probability Example
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Conditional Probability Example

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Conditional Probability – manufacturing example 1. What is the probability that the computer chip was delivered by Manufacturer B given it was defective? P(B|D) = 2. What is the probability that the chip was satisfactory given it was delivered by Manufacturer B? P(S|B) =
Описание слайда:
Conditional Probability – manufacturing example 1. What is the probability that the computer chip was delivered by Manufacturer B given it was defective? P(B|D) = 2. What is the probability that the chip was satisfactory given it was delivered by Manufacturer B? P(S|B) =

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Conditional Probability - example 1. What is the probability that the computer chip was delivered by Manufacturer B given it was defective? P(B|D) = = = 0.625 or 62.5 % 2. What is the probability that the chip was satisfactory given it was delivered by manufacturer B? P(S|B) = = = 0.9498 or 94.98 %
Описание слайда:
Conditional Probability - example 1. What is the probability that the computer chip was delivered by Manufacturer B given it was defective? P(B|D) = = = 0.625 or 62.5 % 2. What is the probability that the chip was satisfactory given it was delivered by manufacturer B? P(S|B) = = = 0.9498 or 94.98 %

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Conditional Probability - example 1. What is the probability that the computer chip was delivered by Manufacturer A given it was defective? P(A|D) = 2. What is the probability that the chip was satisfactory given it was delivered by manufacturer A? P(S|A) =
Описание слайда:
Conditional Probability - example 1. What is the probability that the computer chip was delivered by Manufacturer A given it was defective? P(A|D) = 2. What is the probability that the chip was satisfactory given it was delivered by manufacturer A? P(S|A) =

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Conditional Probability - example 1. What is the probability that the computer chip was delivered by Manufacturer A given it was defective? P(A|D) = = = 0.375 or 37.5 % 2. What is the probability that the chip was satisfactory given it was delivered by manufacturer A? P(S|A) = = = .9800 or 98 %
Описание слайда:
Conditional Probability - example 1. What is the probability that the computer chip was delivered by Manufacturer A given it was defective? P(A|D) = = = 0.375 or 37.5 % 2. What is the probability that the chip was satisfactory given it was delivered by manufacturer A? P(S|A) = = = .9800 or 98 %

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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:
Описание слайда:
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:

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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?
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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?

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Class exercises (continued) Solution: P(promoted│female) = = = .2 or 20% P(promoted│male) = = or 20 % There is no reason to accuse the university for discrimination
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Class exercises (continued) Solution: P(promoted│female) = = = .2 or 20% P(promoted│male) = = or 20 % There is no reason to accuse the university for discrimination

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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
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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

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Statistical independence From our previous example about global warming: Is saying: Global warming is not an issue, independent of the political party the person is a member of? We need to check: If the P(nonissue|republican) = P(nonissue) ? P(nonissue|republican) = = = .57 P(nonissue) = .37 P(nonissue|republican) P(nonissue), therefore the events are not independent
Описание слайда:
Statistical independence From our previous example about global warming: Is saying: Global warming is not an issue, independent of the political party the person is a member of? We need to check: If the P(nonissue|republican) = P(nonissue) ? P(nonissue|republican) = = = .57 P(nonissue) = .37 P(nonissue|republican) P(nonissue), therefore the events are not independent

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Statistical Independence Car example
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Statistical Independence Car example

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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)?
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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)?

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Solution: P = = 0.25 P(A3) = 0.2 P P(A3) They are dependent events P(A1 = = = 0.5 P(A1) = .4 P(A1 P(A1) They are dependent event In general, if one combination of events is independent (or dependent) then the other combinations in the table are independent (or dependent).
Описание слайда:
Solution: P = = 0.25 P(A3) = 0.2 P P(A3) They are dependent events P(A1 = = = 0.5 P(A1) = .4 P(A1 P(A1) They are dependent event In general, if one combination of events is independent (or dependent) then the other combinations in the table are independent (or dependent).

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