Chapter 10: Covariance and Correlation

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Chapter 10 Covariance and Correlation
MATH 3033 based onDekking et al. A Modern
Introduction to Probability and Statistics.
2007Slides by Gustavo OrellanaInstructor
Longin Jan Latecki
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With the rule above we can compute the
expectation of a random variable X with a Bin(n,p)
which can be viewed as sum of Ber(p)
distributions
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Var(X Y) is generally not equal to Var(X)
Var(Y)
If Cov(X,Y) gt 0 , then X and Y are positively
correlated. If Cov(X,Y) lt 0, then X and Y are
negatively correlated. If Cov(X,Y) 0, then X and
Y are uncorrelated.
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In general, EXY is NOT equal to EXEY.
INDEPENDENT VERSUS UNCORRELATED. If two random
variables X and Y are independent, then X and Y
are uncorrelated.
The variance of a random variable with a Bin(n,p)
distribution
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The covariance changes under a change of units
The covariance Cov(X,Y) may not always be
suitable to express the dependence between X and
Y. For this reason, there is a standardized
version of the covariance called the correlation
coefficient of X and Y, which remains unaffected
by a change of units and, therefore, is
dimensionless.