Question

Each front tire on a particular type of vehicle is supposed to be led to a pressure of 26 psl. Suppose the actual pressure in each tire is a random variable for the right tire and for the late with joint pdf given below 22 SXS 32,22 y 32 otherwise (a) Compute the covariance between X and Yound your answer to four decimal place) Cowy (1) Compute the correlation coeficient p for this X and Y. (Hound your answer to four decimal places) P

Answer 1

a) E(X)= ∫2232∫2232 kx(x2+y2) dx dy =				27.3052	=E(Y)
E(X2)= ∫2232∫2232 kx2(x2+y2) dx dy =				753.8493
Var(X)=E(X2)-(E(X))2 =				8.2779	=VAR(Y)
E(XY)= ∫2232∫2232 kxy(x2+y2) dx dy =				745.4783
a) therefore Cov(X,Y)=E(XY)-E(X)*E(Y)=					-0.0931
b)and correlation coefficient ρ =Cov(X,Y)/(σx*σy)=					-0.0112