Question

Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable—X for the right tire and Y for the left tire, with joint pdf given below.

f(x, y) =

K(x2 + y2)		22 ≤ x ≤ 32, 22 ≤ y ≤ 32
0		otherwise

(a) Compute the covariance between X and Y.

(b) Compute the correlation coefficient p for this X and Y.

Answer 1

E(X)= xf(x,y) dx =27.3052 =E(Y)

V(X)= (x-E(x))² f(x,y) dx =8.2779

E(XY)= xyf(x,y) dx =27.3052 =745.4783

a)

covariance between X and Y =Cov(X,Y)=E(XY)-E(X)*E(Y)=-0.0931

b) correlation coefficient p for this X and Y =Cov(X,Y)/sqrt(Var(X)*Var(Y))=-0.0112