Ch 10 Stats
Addition Rule of IID Random Variables
If n random variables (x1, ...) are iid with mean ux and standard deviation ox, then -E(X1...)=nux -Var(x1....)=nsd2 -SD(X1...)=Squareroute of n(sd)
Identically Distributed
Random variables are identically distributed if they have a common probability. -independent from one another -IID-independent and identically distributed -could have different outcome
Uncorrelated
Random variables are uncorrelated if the correlation between them is 0. -if x and y are independent-covariance=0
Multiplication Rule for the Ex. V. of Indep. Variables
The expected value of a product of independent random variables is the product of their expected values. -E(XY)=E(X)E(Y)
Correlation B.w two random variables
is the covariance divided by the product of SDs. -Corr (X,Y)= Cov( X,Y)/Sd1SD2 -no units
Covariance between random variables
is the expected value of the product of deviations from the means Cov (X,Y)=E(x-ux)(Y-uy)
Addition Rule for the Expected Value of a sum of random variables
the expected value of a sum of random variables is the sum of their expected values -E(X+Y)=E(X)+E(Y)
Addition Rule for Weighted Sums
the expected value of a weighted sum of random variables if the weighted sum of the expected values: =E(aX+bY+C)= aE(X)+bE(Y)+C Variance -Var(aX+bY+C)=a2Var(x)+b2Var(y)+2abCov(X,y) is subtracting Var(x-y)=a2Var(x)+b2Var(y)-2abCov(X,y)
Joint Probability Distribution
the probability of two or more random variables taking on specified values simultaneously denoted as P(X=x and Y=y)=P(x,y) -describe the simultaneous outcomes of both random variable -determines whether x and y are independent -probabilities will add because repersent rows or columns
Addition Rule of Variance of Independent Random Variable
the variance of the sum of independent random variables is the sum of their variances -Var(X+Y)=Var(X)+Var(Y)
Addition Rule for variance
the variance of the sum of two random variables is the sum of their variances plus twice their covariance -Var(X+Y)=Var(X)+Var(Y)+2Cov(X,Y)
Independent Random Variables
two random variables are independent if (and only if) the joint probability distribution is the product of the marginal probability distributions. -X and Y are independent> p(x,y)= P(x)xP(y) for all x, y