Stats: Chapter 10
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Chance/Random Phenomenon
Has unpredictable behavior in the short run but has a regular and predictable pattern in the long run

Probability
 Studies the likelihood of occurrence of random events in order to predict the behavior of defined systems.
 Only describes what happens in the long run

Sample Space S
 The set of all possible outcomes in a random phenomenon
 The set of all outcomes are caleld events
 1 event is the subset of the sample space

Probability Model
Description of a random phenomenon consisting of a sample space S and a way of assigning probabilities to events

Probability Rules
 A number between 0  1 is a probability number
 All possible outcomes together must have a probability of one
 If two events have no outcomes in common the probability that one or the other occurs is the sum of their individual probabilities
 The probability that an event occurs is 1 minus the probability that the event does not occur
e.g. If event 1 occurs 50% of the time and a diff event occurs 25% of the time, then the chance of one or the other occuring is 75%

Probability numbers. What does 0, 0.5, and 1 mean?
 0 = never occurs
 1 = always occurs
 0.5 occurs half the trials

0 < P(A) <= 1
A number between 0  1 is a probability number

P(S) = 1
The sample space S always equals 1

P(A or B) = P(A) + P(B)
 If A and B are disjoints if they have no outcomes in common
 The chance of one of them occuring is the sum of the two probabilities

P(A does not occur) = 1  P(A)
The probability of an event that does not occur is 1  the probability that the event does occur

Discrete Probability Model
 A model with a finite sample (has limits)
 The prob of any event is the sum of the probabilities of all the values that make up the event
 This model assigns each of these values a probability between 0 and 1 such that the sum of all the probabilities is 1

Continuous Probability Model
 Assigns the probabilities as areas under a density curve
 The probability of any event is the area under the curve above the values that make up the event

Random Variable
A variable whose value is a numerical outcome of a random phenomenon

Probability Distribution
The random variable X tells us what the possible values of X are and how probabilities are assigned to those values