Random variables X and Y have the following joint probabilit

Random variables, X and Y, have the following joint probability mass function:

Compute the following quantities:

(a) E(X)

(b) E(Y)

(c) E(XY)

(d) Cov(X,Y)

0 0 0.24 0.28 50 0.16 0.10 75 0.120.10 25

Solution

a) E(X) = 0 * 0.52 + 50 * 0.26 + 75 * 0.22

            = 29.5

b) E(Y) = 0 * 0.52 + 25 * 0.48

            = 12

c) E(XY) = 0 * 0* 024 + 0 * 25 * 0.28 + 50 * 0 * 0.16 + 50 * 25 * 0.10 + 75 * 0 * 0.12 + 75 * 25 * 0.1

              = 312.5

d) Cov(X,Y) = E(XY) - E(X) * E(Y)

                    = 312.5 - 29.5 * 12

                    = -41.5