Statistics Study Guide for Test 2 ch.4-5
Statistics Study Guide for Test 2 ch.4-5 Econ 210
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This 10 page Study Guide was uploaded by Erik Arnold Bloomgren on Sunday February 21, 2016. The Study Guide belongs to Econ 210 at University of North Dakota taught by Kristopher Paulson in Winter 2016. Since its upload, it has received 112 views. For similar materials see Intro to bus & economic statistic in Economcs at University of North Dakota.
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Date Created: 02/21/16
Print front and back. P(A) Fold Center-line Cut dashed lines Study like note-cards P(Aͨ ) P(AUB) P(AՈB) P(A B) Σ n N X! Multistep experiments Probability of event A Complement of event A (Probability of every other event) Keyword OR Union of two events Keyword AND Intersection of two events Conditional Property of A given B B occurs first Sum Symbol (as in mathematics) Smaller group of objects or objects taken at a time Overall number of objects Or set of objects Factorial Ex:4!=4*3*2*1=24 0!=1 Process that generates an outcome # of Combinations of N objects # of Permutations for N objects Probability Methods for Assigning Probability Event Complement of Event Union of Two events Intersection of two events Addition Law of Probability Mutually Exclusive Events C N = ( ) = (N!)/[n!(N-n)!] n n N N P n = n!( ) n (N!)/[(N-n)!] Order is important Numerical measure of the likelihood that an event will occscale 0-1 closer to 1 is more likely to occur Classical Method, Relative Frequency Method, and Subjective Method Collection of sample points The event consisting of all sample points that are not in the stated eveex. Ac Event containing all sample points that are in A or B or both The sample points in just the both of events A and B Ex. From a deck of cards, it would be the Red Jacks from events Red cards and Jack cards P(AUB)=P(A)+P(B)-P(AՈB) Events have no sample points in common Addition Law for Mutually Exclusive Events Conditional Probability Multiplication Law of Calculating Intersection Probability Random Variables Discrete Random Variable Continuous Random Variable 2 Conditions for Discrete Probability Function Expected Value of Discrete Random Variable Variance of Discrete Random Variable Standard Deviation of Discrete Random Variable P(AUB)=P(A)+P(B) Does not include P(AՈB) because it equals 0 An event given that another event has occurred P(AՈB)=P(A B)*P(B) So P(A B)=P(AՈB)/P(B) Numerical description of the outcome of an experi- ment Assume either a finite number of values or an infinite sequence of values Assume any numerical value in an interval or collec- tion of intervals 1. f(x)≥0 2. Σf(x)=1 A measure of it’s central location E(x)=µ=Σx*f(x) 2 2 Var(x)=σ =Σ(x-µ) f(x) 2 √(σ )=σ=SD Binomial Distribution Properties of Binomial Distribution Formula for Binomial Distribution Expected Value Binomial Distribution Variance Binomial Distribution Poisson Probability Distribution Poisson Probability Function Permutations Combinations Required Conditions for Discrete Random Variable Discrete probability distribution that provides many applications. See the four properties for a better un- derstanding 1. consists of a sequence of n identical trials; 2. 2 outcomes, success and failure, possible each trial; 3. Probability of a success, denoted by p, does not change from trial to trial; 4. trials are independent; (1-p)=failure f(x)=(n!/[x!(n-x)!)*p (1-p) (n-x) n=# of trials; x=# of success E(x)=µ=np 2 Var(x)=σ =np(1-p) 1. The probability of an occurrence is the same for any two intervals of equal length; 2. The occurrence or nonoccurrence in any interval is independent of the occurrence or nonoccurrence in any other interval x -µ f(x)=[(µ e )/(x!)] f(x)=probability of x occurrences in an interval µ=mean number of occurrences in an interval e=2.71828 Allows to compute the number of experimental out- comes when n objects are to be selected from a set of N objects where the order of selection is important Allows to compute the number of experimental out- comes when the experiment involves selecting n ob- jects from a (usually larger) set of N objects Must be an integer and be infinite or finite number as 1,2,3,4,...ext. Discrete Uniform Probability Function Classical Method Relative Frequency Method Subjective Method e f(x)=(1/n) Assigning probabilities based on the assumption of equally likely outcomes Take frequency divided by total A probability based on a gut feeling. Probabilities are given. So probabilities differ from person to person making a prediction of probabilities e=2.71828
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