Stats exam 2 review PDF

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Stats exam 2 review that is allowed on the test...

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Discrete random variable- X,Y,Z=random variables, x,y,z= possible values of random variables *shown with graph, table or formula and values must be greater than or equal to 0 and p(x) must sum to 1 Function whose domain is the sample space and whose range is all real numbers; dice= { 1,2,3 … 6} List, countable= discrete (counts, money); in an interval= continuous (length, height, mass, volume, time, distance) p(x)= probability distribution; p(x)= P(X=x) expected values of discrete random variables= we want to find pop. Mean and pop. Variance(show central tendency and 2 spread); E(x)=M and M=sum of x*p(x); pop mean is expected value; variance= σ 2 = ∑ (x−M ) p ( x ) ; st. dev you x square root variance Binomial random variable: experiment consists of n identical trials, there are only 2 possible outcomes for each trial (success/failure), probability of success remains the same from trial to trial (denoted by p, F is denoted by q=1-p), the trials are independent, the binomial random variable X is the number of S’s in n trials  If girl is chosen 4/10 then prob. Girl chosen again is 3/10; p changes from trial to trial= not binomial RV  Soda or not is 2 possible outcomes= binomial RV  Households on same block have similar characteristics like income, education, fam size= not random sample, trials are not independent, so not RV n =(n!)/(x!(nA combination gives the number of ways to pick x objects out of n objects without regard to order x x)! n p x q n−x ; x=0,1,2…n where p=prob of a success in a single trial, q=1-p, n=# of trials, x=# of successes in n p(x)= x trials if we know a RV is binomial E(x)=np and σ 2 =npq for binomial RV: X Bin(n,p) Poisson Random Variable: The experiment consists of counting the number of times a certain event occurs during a given unit of time or in a given area or volume (or weight, distance, or any other unit of measurement), The prob that an event occurs in a given unit of time, area, or volume is the same for all the units, The number of events that occur in one unit of time, area, or volume is independent of the number that occur in other units, the mean (or expected) number of events in each unit is denoted by the Greek letter lambda λ Examples of Poisson RVs: The number of traffic accidents per month at a busy intersection, The number of noticeable surface defects (scratches, dents, etc.) found by quality inspectors on a new automobile, The number of parts per million (ppm) of some toxin found in the water or air emissions from a manufacturing plant, the number of diseased trees per acre of a certain woodland, the number of death claims received per day by an insurance company, the number λ2 e−λ Notation: X~Pois( λ ). mean and of unscheduled admissions per day to a hospital P(x)= x! variance= λ P(x ¿ 1 )=1-P(x ≤1 ¿ Continuous random variables= smooth curve denoted by f(x), called probability density function, for cont. P(X=x)=0 Take integral to find area under a curve- P(a15 n Inferences based on a single sample= mu is quantitative p is qualitative xbar − μ Confidence interval for a population mean: normal z statistic z= σ /√ n The probability (.95)= confidence coefficient 95%=confidence level P(Z> Z α /2 )= α /2 Z-alpha is called the critical value. 100(1-alpha)% confidence interval for mu Conditions: random sample from target pop, large sample n>30 or data comes from normal dist, st dev is known “we can be 100(1-alpha) confident that mu lies between the lower and upper bounds of the confidence interval” Confidence interval for a population mean: t statistic xbar − μ *t contains 2 random quantities and must be symmetric, mound-shaped, and with mean 0 t= s/ √ n Large-sample confidence interval for a population proportion When target parameter is a population proportion (p) we use the point estimator phat Mu= p and st dev= pq if nphat>15 and nqhat>15 n pq phat ± Ζ α / 2 n Determining the sample size Ζ α/ 2 σ 2 n=( *always round up ¿ SE in order to estimate a binomial probability (proportion) p with a sampling error SE and % confidence the required Ζ ¿ ¿ α /2¿2 pq ¿ *says mean sample size is n= 2 SE ¿ ¿ ¿ ¿

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