Chapter 4-5
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| definition of experiment | Process by which a measurement is taken or observations are made
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| Examples of experiment | Flipping a coin or rolling a die
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| definition of outcome | the result of an experiment
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| examples of outcomes | Heads or rolling a 3
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| definition of sample space | the listing of all possible outcomes
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| Example of sample space flipping a coin | S={H,T}
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| Definition of event | an outcome or a combo of outcomes
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| Example of event | even number of rolling a die
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| Property 1 | "A probability is always a numerical value between 0 and 1"
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| Property 2 | "The sum of probabilities for all outcomes of an experiment is equal to exactly 1"
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| Empirical approach to probability | experimental
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| Theoretical approach to probability | Classical (dont actually do the experiment)
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| Subjective approach to probability | Expression of confidence (wheatherman)
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| Empirical probability of A= | number of times A occured/ number of trials
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| Law of Large Numbers | The more an even occurs the more the theoretical probablility is true
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| Theoretical probability of A= | number of times A occurs in sample space/ number of the elements in the sample space
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| odds in favor of event A | a to b or a:b
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| odds against event A | b to a or b:a
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| Proability of event A= | a/a+b
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| Probability of event A will not occur= | b/a+b
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| definition of conditional probability | Probability of an event GIVEN another event has occured
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| 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
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| Example of complimentary events | If A is heads the Abar is tails
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| Formula for complimentary events | probability of A compliment= one- probability of A
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| general addition rule: P(A or B)= | P(A)+ P(B)+ P(A and B)
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| general multiplication rule: P(A and B)= | P(A) x P(B given A)
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| definition of mutually exclusive events | Event that share no common elements
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| Example of mutually exclusive events | heads or tails, red or black cards, number 2 and 5
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| P(A and B) in a mutually exclusive event | 0
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| Definition of an independent event | The occurrence or nonoccurrence of one gives us no information about the likliness of occurrence for the other.
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| Formula for an independent event | P(A)= P(A given B)= P(A not given B)
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| definition of dependent events | Occurrence of 1 event does have an effect on the probability of occurrence of the other event
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| Special Multiplication rule | In 2 independent events P(A and B)=P(A) x P(B)
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| 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
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| example of random variable | x={0,1,2}
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| definition of discrete random variable | A quantitative random variable that can assume a countable number of values.
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| definition of continuous random variable | A quantitative random variable that can assume an uncountable number of values.
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| example of discrete random variable | number of heads when we flip a coin 10 times
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| example of continuous random variable | distance from earth center to sun center.
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| 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
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| 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
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| definition of probability function | A rule P(x) that assigns probabilities to the values of the random variable x
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| sigma squared | variance
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| sigma | standard deviation
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| MU | mean
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| definition of binomial experiment | an experiment with only 2 outcomes (success of failure). the trials are independent. p= success.
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| MU in a binomial distribution | np
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| variance in a binomial distribution | np(1-p)
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