Learn / Library / Statistics

Covariance of paired points

StatisticsEasy

A pair of price moves $(X, Y)$ takes each of the values $(1, 2)$ , $(2, 1)$ , $(3, 5)$ and $(4, 4)$ with probability $\frac{1}{4}$ . What is $Cov (X, Y)$ ?

Checking an answer needs JavaScript. The hint and the solution open without it.

Hint

Use the identity that covariance is the mean of the product minus the product of the means.

Solution

The means are $E [X] = \frac{5}{2}$ and $E [Y] = 3$ .
The mean of the product is $E [X Y] = \frac{2 + 2 + 15 + 16}{4} = \frac{35}{4}$ .
Subtracting the product of the means gives $\frac{35}{4} - \frac{15}{2}$ , so the covariance is $\frac{5}{4}$ .

Answer: $\frac{5}{4}$

Next question Back to the library