Statistics Exam 3

Simulation

A technique used to re-create a random event.

Can be tactile or virtual

Measures how often a certain outcome is observed.

Random Process

Represents scenarios where the outcome og f any particular trial of an experiment is unknown, but the proportion (relative frequency) a particular outcomes is observed approaches a specific value as the number of trials increase.

Probablility

Measure of hte liklihood of a random phenomenon or chance behavior occuring.

Short-Term

Outcomes

Long-term predictability

The Law of Large NUmbers

Number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the probability of the outcome.

Experiment

Any process with uncertain results that can be repeated.

Sample Space

S

of a probaility experiment is the collection of possible outcomes.

Ex: 6 sided dice is sample (1-6)

Event

Any collection of outcomes from a porbability experiment.

One outcome or more

One = Simple events e with coeffiecnt i

Two= E

P(E)

Probability of an event.

Rules of Probability

1.) Any Event E (P(E)) must be greater thatn or equal to 0 and less than or equal to one!

.—> Will always be between 0-1

2.) The sum of the probabilities of all outcomes must equal 1. So all of the samples must equal one.

—> Use the dice example. each side can happen (1/6) times. When you add them it equals one! If it is .999999 It is okay!

Probability Model

Lists the possible outcomes of a probability experiment adn each outcome’s probability. Im

Impossible

The probability of an event is zero

Certainty

The probability of the event is one

Unusual event

An event that has a low probability of occuring

Less than 0.05 is usually the cutoff.

Probability of an event: Empirical Method

Approximately the number of times event E is observed by the number of repetitions of the experiment.

P(E) = Relative Frequency/Number of trials of experiment.

Classical Method

Experiment will have equally likely outcomes when each single event has the same probability of occurring.

P(E) = N (E) number of outcomes/N(S) Number of outcomes in the sample space

Tree Diagram

List the equally likely outcomes

Subjective Probability

An Outcome is a probability obtained on the basis of personal judgment

Ex: Sports reporter predicting there is a 20% chance the Red Sox will play in the world series. (No specific numbers)