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 K(x2 y2 22 x 31, 22 < y s 31 f(x, у) %3D otherwise (a) Compute the covariance between X and Y. (Round your answer to four decimal places.) Cov(X, Y) (b) Compute the correlation coefficient p for this X and Y. (Round your answer to four decimal places.) р 3

Answer 1

a) E(X)= ∫2231∫2231 kx(x2+y2) dx dy =				26.7523	=E(Y)
E(X2)= ∫2231\∫2231 kx2(x2+y2) dx dy =				722.3972
Var(X)=E(X2)-(E(X))2 =				6.7121	=VAR(Y)
E(XY)= ∫2231∫2231 kxy(x2+y2) dx dy =				715.6215
a) therefore Cov(X,Y)=E(XY)-E(X)*E(Y)=					-0.0637
b) and correlation coefficient ρ =Cov(X,Y)/(σx*σy)=					-0.0095