# STA 3381 Study Guide - Comprehensive Final Exam Guide - Test Cricket, Old Testament, Factorial

187 views56 pages
20 Nov 2018
School
Course
Professor
STA 3381
Unlock document

This preview shows pages 1-3 of the document.
Unlock all 56 pages and 3 million more documents.

Unlock document

This preview shows pages 1-3 of the document.
Unlock all 56 pages and 3 million more documents.

2.1
Experiment-ξ anything that can have an uncertain outcome
Sample spaceξ - set of all possible outcomes of the experiment
Simple experiment only has 2 outcomes
Weld is either defective of not defective.
Eventsξ - any collection (subset) of outcomes contained in the sample space S.
ξSimpleξ if contains one outcome, ξcompoundξ if it contains more than one outcome
Size of the sample space is the number of simple events.
Ex: experiment to find which outcomes will have at least one defective weld β for set S={NNN, DNN,
NDN, NND, NDD, DND, DDN DDD} only the ones that include a D.
Complementsξ of an event Aβ is the complement of A
Unionξ of two events A Bξ©
Intersectionξ of two events A Cξ¨
( A C)β β do whatβs inside the parhenthesis first!ξ¨
No enclosures required if doing repetitive intersections and unions
If there are no outcomes in common (ξmutuallyξ ξexclusiveξ or ξdisjointξ event), theree are no values that fall
in the set, so it is aξ null setξ. Denoted by β
A B = (A and B are mutually exclusive or disjoint events)ξ¨ β
visual representation
Rectangle includes the whole sample space
An event is represented by a circle
2.2
Three basic rules (axioms) of probability
* Even if I had A1 A2 A3, (FINITE), the rule still applies.
β If something has to happen, it has probability 1. A certain event.
find more resources at oneclass.com
find more resources at oneclass.com
Unlock document

This preview shows pages 1-3 of the document.
Unlock all 56 pages and 3 million more documents.

β If a set has nothing in it, there is no probability of occurance
β P( =0)β
β Probability will always equal 1 if it canβt happen at the same time.
β Any probabililty we have can only be 0 and 1.
Battery example
If multiple events repeated over and over again, then just multiply the events.
Probability of success on first try: P(E1)=0.99
Probabililty of success on second try: P(E2)=(0.01)(0.99)
P(E3)=(0.01)^2*(0.99)
P(Ei)=0.01^(i-1)*0.99
β a is probabilty of sucess, r is failure
β
β n(A) denotes the number of replications on which A does occur
β The ratio ξn(A)/n is called the ξrelative frequency
ξ
ξof occurance of the event A in
the sequence of n replications
Package example
β For example, Package #3
β n(A)/n = β=0.667
Long term probability, as the number of replications increase, the frequency stabilizes. Converge to a
specific number. The number it converges to is ξlimiting (or long-run) frequency
ξ
of the event A.
β It depends on how long it takes to converge.
β As the number increases, the long rul value is going to become more accuracy
Package arrival example
60 percent is the limiting frequency, so overall 60% of the packages arrive on first day. Not exactly 60%,
but we can expect that to happen.
For any event A, P(A)+P(Aβ)=1, from which P(A)=1-P(Aβ).
For batter ex, P(success)=1-P(failure)
0.99=1-P(failure)
find more resources at oneclass.com
find more resources at oneclass.com
Unlock document

This preview shows pages 1-3 of the document.
Unlock all 56 pages and 3 million more documents.