Econometrics Econ. 504

1. EconometricsEcon. 504 Chapter 3: Getting the Hang of Statistics

2. I. What is Special about Random Variables

5. 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

8. 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

9. 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)

10. 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)

11. B A

12. C D

13. F E