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Administrative Studies
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ADMS 2320
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Michael Rochon
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Lecture

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Administrative Studies

ADMS 2320

Michael Rochon

Fall

Description

Chapter 6
Pr robbaabbi iityy
6.2 Assigning probabilities to Events
• –acrientxperiment ss or course of action, whose
outcome is uncertain.
• Examples
Experiment Outcomes
etdeocrtsia•ttmarksTaanNumbers between 0 and 100
eteeaasbernufmom
a computer
6.2 Assigning probabilities to Events
• Performing the same random experiment
repeatedly, may result in different outcomes,
probability of occurrence of a certain outcome.
•and list the possible outcomes first.o define
1 Sample Space
• Determining the outcomes.
–Bdinevlllotomes.
–Makettltomesayuvie.
• A list of outcomes that meets the two conditions
abbovvee s ccalledd a saampple sspaace..
Sample Space: S = {O , O ,…,O } 1 2 k
O
1 O 2
Sample Space Simple Events
a sample space of a The individual
random experiment outcomes are called
is a list of all possible simple events.
experiment. Thetthhee An event is any collectionSimppllee eevveennttss ccaannnnoott
outcomes must be Ouof one or more simple events further
mutually exclusive adetermine P(A), the decomposed
exhaustive. into constituent
probability that event A outcomes.
will occur.
Assigning Probabilities
–GvienalspaceS={ O ,O ,…,O }, the following
1 2 k
characteristics for the probability P(i) of the simple
event O iust hold:
1. 0 d P ▯O▯ d1 for each i
i
kk
2. ¦ P ▯O▯i 1
i 1
–Prolfi:thtili(a A) of event
A is the sum of the probabilities assigned to the
simple events contained in A.
2 Approaches to Assigning Probabilities and Interpretation of Probability
•r
–Thelalpproach(gam es of chance – coin toss)
–Thelfquencyainailie(ass
based on history of outcomes)
–Thesviteapproach(w e assign probabilities based
on a degree of belief)
nitrtI
–afIranrisirte epeated an infinite number of
times, the relative frequency for any given outcome is the
probability of this outcome.
6.2 Joint, Marginal, and Conditional Probability
• We study methods to determine probabilities of
events that result from combining other events in
various ways.
• There are several types of combinations and
relationship ps between events:
–ntrifvtns
–Unieftens
–Depenatidepettens
–Complmetvent
Intersection
• The intersection of event A and B is the event that
occurs when both A and B occur.
• The intersection of events A and B is denoted by (A and
B)).
• The joint probability of A and B is the probability of the
intersection of A and B, which is denoted by P(A and B)
3 Intersection
• Example 6.1 (pg. 182)
–Apoalerxaihtlipiteen
the performance of mutual funds and the school the fund
manager earned his/her MBA.
–Thofitldbrtitail.i
Mutual fund Mutual fund doesn’t
outperformthe market outperformthe
market
Top 20 MBA program
.11 .29
Not top 20 MBAprogram .06 .54
Intersection
• Example 6.1 (pg. 182) –continued
–Thotrtilfi P(A1and B 1
[mutual fund outperform…] and […from a top 20 …] = .11
yTijeh
[mutual fund outperform…] and […not from a top 20 …] = .06
Mutual fund Mutual fund doesn’t
outperformsthe outperformthe market
market (B2
(B1)
Top 20 MBA program 1)A .11 .29
Not top 20 MBAprogram (A ) 2 .06 .54
Intersection
• Example 6.1 (pg. 182) –continued
–Thotrtilfi P(A1and B 1
[mutual fund outperform…] and […from a top 20 …] = .11
yTijeh
[mutual fund outperform…] and […not from a top 20 …] = .06
P(A aanndB ))
2 1
Mutual fund Mutual fund doesn’t
outperformsthe market outperformthe market
(B ) (B2)
1
Top 20 MBA program 1) .11 .29
Not top 20 MBAprogram (A ) 2 .06 .54
4 Marginal Probability
• Example 6.1 (pg. 183)
• These probabilities are computed by adding
across rows and down columns
Muttfuladl fund Muttfuladl fund Mairlginal
outperformsthe doesn’toutperform Prob.
market (B1) the market (B2) P(Ai
Top 20 MBA program (A)1 P(A 1nd B )+1P(A an1 B ) 2 = P(A ) 1
Not top 20 MBAprogram (A 2) P(A 2nd B )+1P(A an2 B ) 2 = P(A ) 2
Marginal Probability P(j)
Marginal Probability
• Example 6.1 (pg. 183)
• These probabilities are computed by adding
across rows and down columns
Muttfuladl fundMuttfuladl fund Mairlginal
outperforms doesn’t Prob.
the market outperformthe P(Ai
(B1 market (B 2)
Top 20 MBA program (A 1) .11 + .29 = .40
Not top 20 MBAprogram .06 + .54 = .60
(A2)
Marginal Probability P(B)
j
Marginal Probability
• Example 6.1 (pg. 183)
• These probabilities are computed by adding
across rows and down columns
Muttfuladl fund Muttfuladl fund Mairlginal
outperformsthe doesn’toutperform Prob.
market (B1) the market (B2) P(Ai
Top 20 MBA program (A)
1 P(A 1nd B )1 P(A1and B 2 .40
Not top 20 MBAprogram (A ) + +
2 P(A2 =nd B1 P(A 2=nd B 2 .60
Marginal Probability P(B) P(B ) P(B )
j 1 2
5 Marginal Probability
• Example 6.1 (pg. 183)
• These probabilities are computed by adding
across rows and down columns
Muttfuladl fund Muttfuladl fund Mairlginal
outperformsthe doesn’toutperform Prob.
market (B 1 the market (B2) P(A)
i
Top 20 MBA program (A) 1 .11 .29 .40
+ +
Not top 20 MBAprogram (A )2 .06 .54 .60
Marginal Probability P(B) .17 .83
j
Marginal Probability
• Example 6.1 (pg. 183)
• These probabilities are computed by adding
across rows and down columns
Muttfuladl fund Muttfuladl fund Mairlginal
outperformsthe doesn’toutperform Prob.
market (B 1 the market (B2) P(A i
Top 20 MBA program (A)
1 .11 .29 .40
Not top 20 MBAprogram (A ) .06 .54 .60
2
Marginal Probability P(j) .17 .83 1.00
Notice that the sum of the marginal row and column equal 1
Conditional Probability
• Example 6.2 on pg184 (Example 6.1 –
continued)
tfdiib
is managed by a “Top 20 MBA Program graduate”, given that
it did not outperform the market.
– First you want to locate the conditional rules of probability on
page 178
–Ntt 1|B2) converts into P(A 1nd B ) 2
P(B 2
–Wnditoltnvsn
6 Conditional Probability
• Example 6.2 on pg184 (Example 6.1 –
continued)
–Fitedipliliatb y that a randomly selected
fund is managed by a “Top 20 MBA Program graduate”,
given that it did not outperform the market.
• Solution
P(A 1B )2P(= and 1 ) 2 = .29 = .3494
3 P8 (B ) .
2
Conditional Probability
• Example 6.2 on pg.184
ayldiib
is managed by a “Top 20 MBA Program graduate”, given that
it did not outperform the market.
• Solution Mutual fund Mutual fund Marginal
outpperform doesn’t Prob.
s the outperform
P(A1|2 ) = market (B) the market P(Ai
1 (B )
P(A1and B2) 2
P(B2) Top 20 MBA program .11 .29 .40
(1 )
=.29/.83 Not top 20 MBA .06 .54 .60
program (2 )
= .3494 Marginal Probability .17 .83
P(B) .83
j
Conditional Probability – Dependent Events
• Before the new information becomes available we
have
P(A ) = 0.40
1
• After the new information becomes available
P((A )) changes to
1
P(A |1B ) =2.3494
• Sin

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