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Stats Exam #2
Chapter 4-5
| Question | Answer |
|---|---|
| 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
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