# Stat 332 Cards exam 1

 Population The entire collection of objects or outcomes about which information is sought Sample A subset of a population containing the objects or outcomes that are actually observed. Simple Random Sample of size n is a sample chosen by a method in which each collection of n population items is equally likely to comprise the sample, just as in a lottery Bias difference between sample and population Conceptual Population A population that consists of all values that could possibly be observed, from which a simple random sample comes Experiment An experiment is any procedure that can be infinitely repeated and has a well defined set of outcomes Sampling Variation variation due to performing the experiment Response Variable Outcome (Dependent Variabel)example: mpg Factor quantity changed (Independent Variable)example: driving style Levels exact value of the factorexample: windows up/down sample mean Xbar = 1/n { summation (x1 , x2 , ..xn) } Sampling Variance S2= 1/(n-1) { sum 1 to n (xi - xbar) } 2 Sample Standard Deviation s= { sqrt (s2) } Sample Median Middle of ORDERED data Dotplot . . . . . ... . .. . . ________________ Histogram the thing with lots of bars and each represents a spread of values like 6-10 or 11-15 box plot learn how to make these.. IQR? Barplot do instead of piechart each bar is a percent of total observed, so all are < 1 Sample Space Lits of all possible values Event A subset of the Sample Space Union A or B or Both"A U B" Intersection A and B"A ∏ B" Complement Not AAc Mutually Exclusive Nothing in Common Axioms of Probability i P(Sample space) = 1ii P(A) ≥ 0iii if A and B are Mutually Exclusive, P(A U B) = P(A) + P(B) Additive Rule P(A U B) = P(A) + P(B) - P( A ∏ B) Number of ways to perform k tasks n1, n2, .....nk Permutation number of ways to choose within group where order mattersn! / (n-k)! Combination n! / (k!(n-k)!) Conditional Probability P(A l B)which is P(A "given" B) Independence P(A l B) = P(A) Multiplicative Rule P( A ∏ B) = P(B) x P(A l B) Definition of a Random Variable quantity that takes on different values with different possibilities numerical Characteristics of a discrete random variable discrete, countably infinite possible values Probability Mass FUnction P(x) = P(X=x) = P(X= specific thing) Mean of a discrete random variable µx = { sum all poss (X x p(x)) } Variance of a Discrete Random Variable sigma2 = {sum. all possible (x-µ)2 x p(x) Standard Deviation of a Discrete Random Variable sigma = {sqrt (sigma2)}standev disc rand var = sqrt variace disc rand var Characteristics of a Continuous Random Variable Takes on different possible values with different possible probabilities (on the interval) Probability Density Function Probability is Area under P(a < x < b) = {integral a to b ( f(t) dt) } Mean of a Continuous Random Variable µx = integral -infinity to infinity (x f(x) Variance of Continuous Random Variable sigma2 = {integral -inf to +inf [ (x-µ)2 x f(x) dx] } Standard dev of a cont random variable sigma = {sqrt (sigma2)} Probability Mass Function of Bernoulli (p) P(x) = (1-p if x=0) ( p if x=1) Mean of Bernoulli p Variance of Bernoulli p(1-p) Characteristics of Binomial (n,p) x ~ Binomial (n,p) Probability Mass Function of Binomial (n,p) P(x) = (nx) px(1-p)n-x if x = 0,1,2....n 0 otherwise Mean of Binomial (n,p) µx = np variance of Binomial(n,p) sigma2x = np(1-p) Probability mass function of Poisson (lambda) P(x) = e-lambda (lambdax/x!) if x = 0,1,2,.... 0 otherwise mean of Poisson (lambda) µx = lambda Variance of Poisson (lambda) sigma2x= lambda Charactersitics of N (µ,sigma2) N is normal, µx = µ ..... sigma2 = sigma2 empirical rule 68% will fall within 1 standev95% will fall within 2 standev99.7% will fall within 3 standev Z-score table A.2 compute probabilities of Lognormal (µ, sigma2) if take log of lognormal you get normal AuthorAnonymous ID7767 Card SetStat 332 Cards exam 1 Descriptioncards for the first test based on his handout. Updated2010-02-23T01:26:44Z Show Answers