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# Stats Exam #2

### Chapter 4-5

definition of experiment Process by which a measurement is taken or observations are made
Examples of experiment Flipping a coin or rolling a die
definition of outcome the result of an experiment
examples of outcomes Heads or rolling a 3
definition of sample space the listing of all possible outcomes
Example of sample space flipping a coin S={H,T}
Definition of event an outcome or a combo of outcomes
Example of event even number of rolling a die
Property 1 "A probability is always a numerical value between 0 and 1"
Property 2 "The sum of probabilities for all outcomes of an experiment is equal to exactly 1"
Empirical approach to probability experimental
Theoretical approach to probability Classical (dont actually do the experiment)
Subjective approach to probability Expression of confidence (wheatherman)
Empirical probability of A= number of times A occured/ number of trials
Law of Large Numbers The more an even occurs the more the theoretical probablility is true
Theoretical probability of A= number of times A occurs in sample space/ number of the elements in the sample space
odds in favor of event A a to b or a:b
odds against event A b to a or b:a
Proability of event A= a/a+b
Probability of event A will not occur= b/a+b
definition of conditional probability Probability of an event GIVEN another event has occured
definition of complimentary evnet The compliment of A, Abar is the set of all sample points in the sample space that does not belong to event A
Example of complimentary events If A is heads the Abar is tails
Formula for complimentary events probability of A compliment= one- probability of A
general addition rule: P(A or B)= P(A)+ P(B)+ P(A and B)
general multiplication rule: P(A and B)= P(A) x P(B given A)
definition of mutually exclusive events Event that share no common elements
Example of mutually exclusive events heads or tails, red or black cards, number 2 and 5
P(A and B) in a mutually exclusive event 0
Definition of an independent event The occurrence or nonoccurrence of one gives us no information about the likliness of occurrence for the other.
Formula for an independent event P(A)= P(A given B)= P(A not given B)
definition of dependent events Occurrence of 1 event does have an effect on the probability of occurrence of the other event
Special Multiplication rule In 2 independent events P(A and B)=P(A) x P(B)
definition of random variables A variable that assumes a unique numerical value for each of he outcomes in the sample space of a probability experiment
example of random variable x={0,1,2}
definition of discrete random variable A quantitative random variable that can assume a countable number of values.
definition of continuous random variable A quantitative random variable that can assume an uncountable number of values.
example of discrete random variable number of heads when we flip a coin 10 times
example of continuous random variable distance from earth center to sun center.
definition of probability distribution A set of probabilities associated with each of the values of a random variable. it is a theoretical distribution used to represent populations
ways to determine if there is a probability distribution 1) each probability is between 0 and 1 2) the sum of the probabilities is 1
definition of probability function A rule P(x) that assigns probabilities to the values of the random variable x
sigma squared variance
sigma standard deviation
MU mean
definition of binomial experiment an experiment with only 2 outcomes (success of failure). the trials are independent. p= success.
MU in a binomial distribution np
variance in a binomial distribution np(1-p)
Created by: o123runner321o