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### 50 Cards in this Set

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 Variance (1/(n-1))*sum(xi-x)^2 Standard Deviation square root of variance Five-Number Summary Minimum Q1 Mean Q2 Maximum Density function describes a density curve in functional form (defined over all possible values the variable can take) Normal Distribution 1) has a "bell shape" 2) mean=median=mode 3) symmetric 4) inflection pts at m+sd, m-sd Rule for Normal Distribution 65-95-99.7 Z-Score z= (x-m)/sd Standard Normal Distribution Normal distribution N(0,1) with mean 0 and standard dev 1 If a varable x has any Normal distribution with mean M and standard dev, the standardized variable z has the standard normal distribution Covariance S2XY = (1/n-1)sum (xi - x)(yi - y) Correlation Cov(X,Y)/SxSy Least-Squares Regression Line equations on sheet Lurking variable variable that is not among the explanatory or response variables yet may influence the interpretation of relationships among variables Simpson's Paradox an association or comparison that holds for all of several groups can reverse direction when the data are combined to form a single group Simple Random Sample consists of n individuals from the population chosen in such a way that every set of n indivviduals has an equal chance to be the sample actually selected Sampling Distribution distribution of values taken by the statistic in all possible samples of the same size from the same population Probability Rules 1. Probability of any event A satisfies 0<=P(A)<=1 2. If S is the sample space in a probability model, P(S)=1 3. the complement of any event A is the event that A does not occur, written as A^C P(A does not occur)=1-P(A) 4. Two events A &B are disjoint if they have no outcomes in common and therefore cannot occur simultaneously P(A or B)=P(A)+P(B) Rules for Means 1. If x is a random varaible and a and b are fixed numbers, then M(a+bx)=a+BMx 2. If x and y are random varialbe, then M(x+y)=Mx+My Variance for Discrete and Continuous Variables E(X^2)-M^2 Rules for Variances 1. V(a+bx)=b^2V(x) 2. If X&Y are independent V(x+y)=V(x)+V(Y) V(x-y)=V(x)-V(Y) 3. If X&Y have correlation p, V(x+y)=V(x)+V(y)+2pV(x)V(y) V(x-y)=V(x)+V(y)-2pV(x)V(y) Covariance of Two Random Variables Cov(XY)=E(XY)-MxMy Correlation Between X&Y Cov(XY)/(sdX*sdY) Joint Probability Function f(x0,y0)=P{X=x0 and Y=y0) Marginal Probability Function fx(x0)=P(x=x0)=sum over yi of f(x0,yi) Joint Probability Funciton for continuous variable To find P{x1