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Final

STAT1008 Study Guide - Binomial Coefficient, Random Variable, Standard Deviation

3 Pages
93 Views
Summer 2017

Department
Statistics
Course Code
STAT1008
Professor
Bronwyn
Study Guide
Final

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Probability
11.1 Probability Rules
Event soethig that either happes or does’t happe is true or is ot true.
Probability of event (A) is the long-run frequency or proportion of times the event occurs.
Probability always between O and 1.
P(A) = 1 means A will definitively happen.
P(A) = 0 means A will definitively not happen.
If there are equally likely outcomes, then P(A) = no. of outcomes of event A/total no. of
outcomes.
Combination of Events
P (A and B), or P (A or B).
Additive Rule
P (A or B) = P(A) + P(B) P(A&B).
Use Venn diagram.
Complement Rule
P (not A) = 1 P(A).
P (not (A or B)) = 1 [P(A) + P(B) P(A and B)]
Conditional Probability
P (A if B) = P(A and B)/P(B), is the probability of A, if we know B
has happened.
You may also see this written as P (A I B).
This is read i ultiple ays: proaility of A if B, proaility
of A gie B or proaility of A oditioal o B.
Note: P (A if B) ≠ PB if A.
Multiplicative Rule
P (A and B) = P (A if B) P (B).
Equivalent form: P (A and B) = P (A) P (B if A).
Special Case: Disjoint
Events
Events A and B are disjoint or mutually exclusive if only one of
the two events can happen.
If A and B are disjoint, then P (A or B) = P (A) + P(B).
If A and B are disjoint, then both cannot happen, so P(A and B) =
0.
Special Case:
Independent Events
Events A and B are independent if P (A if B) = P (A).
Intuitively, knowing that event B happened does not change the
probability that event A happened.
If A and B are independent, then P (A and B) = P(A)P(B).
11.2 Tree Diagrams and Bayes' Rule
Total Probability Rule
For any two events A and B, P(B) = P(A and B) + P(not A and B) = P(A)P(B if A) + P(not A)P(B if
not A).
If events B1, B2, through Bn are disjoint and together make up all possibilities, then: P(A) = P(A
and B1) + P(A and B2 + … + PA ad Bn).
Tree Diagrams
The initial set of branches show the probabilities from one set of events and the second set of
branches show conditional probabilities.
Multiplying along any set of branches uses the multiplicative rule to find the joint probability
for that pair of events.
Bayes' Rule
If A and B are any two events:
P(A if B) = P(A and B)/P(B)
Bayes’ Rule arious fors:
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Description
Probability 11.1 Probability Rules Event something that either happens or doesnt happen (is true or is not true). Probability of event (A) is the long-run frequency or proportion of times the event occurs. Probability always between O and 1. P(A) = 1 means A will definitively happen. P(A) = 0 means A will definitively not happen. If there are equally likely outcomes, then P(A) = no. of outcomes of event A/total no. of outcomes. Combination of Events P (A and B), or P (A or B). Additive Rule P (A or B) = P(A) + P(B) P(A&B). Use Venn diagram. Complement Rule P (not A) = 1 P(A). P (not (A or B)) = 1 [P(A) + P(B) P(A and B)] Conditional Probability P (A if B) = P(A and B)/P(B), is the probability of A, if we know B has happened. You may also see this written as P (A I B). This is read in multiple ways: probability of A if B, probability of A given B or probability of A conditional on B. Note: P (A if B) P(B if A). Multiplicative Rule P (A and B) = P (A if B) P (B). Equivalent form: P (A and B) = P (A) P (B if A). Special Case: Disjoint Events A and B are disjoint or mutually exclusive if only one of Events the two events can happen. If A and B are disjoint, then P (A or B) = P (A) + P(B). If A and B are disjoint, then both cannot happen, so P(A and B) = 0. Special Case: Events A and B are independent if P (A if B) = P (A). Independent Events Intuitively, knowing that event B happened does not change the probability that event A happened. If A and B are independent, then P (A and B) = P(A)P(B). 11.2 Tree Diagrams and Bayes' Rule Total Probability Rule For any two events A and B, P(B) = P(A and B) + P(not A and B) = P(A)P(B if A) + P(not A)P(B if not A). If events B1, 2 , through n are disjoint and together make up all possibilities, then: P(A) = P(A and B 1 + P(A and B 2 + + P(A and B n. Tree Diagrams The initial set of branches show the probabilities from one set of events and the second set of branches show conditional probabilities. Multiplying along any set of branches uses the multiplicative rule to find the joint probability for that pair of events. Bayes' Rule If A and B are any two events: P(A if B) = P(A and B)/P(B) Bayes Rule various forms:
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