The weight W in pounds and the height H in inches of a rando

The weight W in pounds and the height H in inches of a randomly chosen high-school football player can be modeled as continuous random variables uniformly distributed on the intervals [185, 215] and [67, 73], respectively. It is also known that the correlation coefficient p for these random variables has value 1/3. Compute E[W H].

Solution

E(W)=(185+215)/2 = 200

E(H) = (67+73)/2 = 70

rho = 1/3

Cov(W,H) = E(WH)-E(W)E(H)

SD(W) = 8.66 and SD(H) = 1.73(From formula of uniform distribution)

Therefore, Cov(W,H) = (1/3)*8.66*1.73 = 4.99

Using the formula given above, E(XY) = 4.99+200*70 = 14004.99