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Econometrics
Econ. 405
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
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
 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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