Chapter 3: Getting the Hang of Statistics Econometrics Econ. 504 Chapter 3: Getting the Hang of Statistics

I. What is Special about Random Variables  

 

 

II. Other Useful Measures 1) Variance Variance provides a measure of dispersion (measures how far a set of random numbers are spread out from their mean). Variance is the average of the squared differences from the Mean. Variance is used to produce standard deviation. The variance of a constant is: Var (a) = 0

 

 

Cov(X, Y) = E {[X - E(X)] [Y - E(Y)]} 3) Covariance Covariance uses the difference between the value of each random variable and its mean to determine how they vary with one another. The Covariance is: Cov(X, Y) = E {[X - E(X)] [Y - E(Y)]} Where: E{X} = mean of X E{Y} = mean of Y

if f(X\Y)= f(X) or f(X,Y)=f(X).f(Y) Covariance of two independent random variables is: Cov(X, Y) = 0 if f(X\Y)= f(X) or f(X,Y)=f(X).f(Y) Covariance of two random variables multiplied by a constant is: Cov(aX, bY) = ab Cov(X, Y) Covariance of a random variable times its self is: Cov(X, X) = Var(X)

4) Correlation It measures the strength of the relationship between two variables. To calculate the correlation coefficient for two variables (X, Y), we would use the covariance formula, shown below: Corr (X, Y) = Cov (X,Y) / Sd(X) Sd(Y)

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