Introduction to Probability
4e. Covariance and correlation
4. Expectation and variance
Covariance and correlation coefficient: equivalent definitions.
[Si] "Expected value" : Sect 3 "Covariance and correlation" : Items
"Definition"
,
"Properties"
.
[BT]
: Sect 4.5 "Covariance and correlation".
Basic properties. Linear transformations. Bilinearity of covariance. Variance and covariance.
[Si] "Expected value" : Sect 3 "Covariance and correlation" : Item
"Properties"
.
Zero correlation and symmetry.
Zero correlation and independence.
[BT]
: Sect 4.5 "Covariance and correlation".
Variance of a sum.
[Si] "Expected value" : Sect 3 "Covariance and correlation" : Item
"Variance of a sum"
.
[BT]
: Sect 4.5 "Covariance and correlation" : Item "Variance of the sum of random variables".
Sum of indicators. Variance of hypergeometric random variables.
Least squares: the best linear predictor.
[Si] "Expected value" : Sect 3 "Covariance and correlation" : Item
"The best linear predictor"
.
[BT]
: Sect 4.6 "Least squares estimation" : Item "Linear least mean squares estimation based on a single measurement" (p. 246-).
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