covariance and correlation

Question 1

covariance

Answer 1

the strength of dependence;
Cov(X,Y) =sum((x - mean(x))*(y - mean(y))px,y(x,y)) = E(XY) - E(X)E(Y); IF X and Y are independent their coverage is zero

Question 2

Correlation

Answer 2

measure of dependance that is scale-independent;
Cor(X,Y) = Cov(X,Y) / sqrt(Var(X)*Var(Y))’
cor(x,y) = 1 - means perfect positive correlation
cor(x,y) = 0 - no correlation
cor(x,y) = -1 perfect negative correlation

Question 3

the variance of x + y

Answer 3

Var(aX +/- bY) = a^2Var(X) + b^2Var(Y) +/- 2abCov(X,Y)

Question 4

Properties of covariance and correlation

Answer 4

Cov(x,x) = Var(x)

Cov(ax + b, cy + d) = acCov(X,Y)