Write covariance and correlation formulas.

easy

Answer

$\operatorname{Cov}(X, \;Y)\; = \;E[(X\; - \;{\mu}_{X})(Y\; - \;{\mu}_{Y})]\; = \;E[\mathrm{XY}]\; - \;E[X]$
$\operatorname{Corr}(X, \;Y)\; = \;{\rho}\; = \;\operatorname{Cov}(X, \;Y)\; / \;({\sigma}_{X}\;{\sigma}_{Y})$
$Sample versions: divide by n-1 (unbiased).$
$Correlation is scale-invariant; covariance has weird units (product of X and Y units).$
$\mathrm{guarantees}\; \mid \operatorname{Cov}(X, Y)$

Check yourself — multiple choice

Cov = E[X]·E[Y]
Cov = E[XY] - E[X]E[Y]; ${\rho}\; = \;\operatorname{Cov} / ({\sigma}_{X}\;{\sigma}_{Y})$ ∈ [-1,1]; correlation is scale-invariant
Correlation unbounded
Cov > 1 always

Cov = E[XY]-E[X]E[Y]; correlation scaled to [-1,1] by SDs.

#variance#probability

215 interview questions in this topic.