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

STA 3381

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.

ξSimpleξ if contains one outcome, ξcompoundξ 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 whatβs inside the parhenthesis first!ξ¨

(A C) Bβξ© ξ¨

No enclosures required if doing repetitive intersections and unions

If there are no outcomes in common (ξmutuallyξ ξexclusiveξ or ξdisjointξ 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

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 canβt 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 ξn(A)/n is called the ξrelative frequency

ξ

ξof 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 ξlimiting (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