Each front tire of a particular type of child's toy vehicle is supposed to be filled to a pressure of 1.6 pounds per square inch(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 f(x,y)= (2*(x3+y3))/15 for 1<= x<=2, 1<=y<=2 = 0 otherwise
a) Determine the marginal density of the air pressure in the right tire alone(be sure to state the domain).Are X and Y independent? why or why not?
b) Find the conditional density fX|Y(x|y). be sure to state the domain
c) What is the expected tire pressure of the right tire? find E[XY]
d) Find cov(X,Y). are X and Y positively correlated, negatively correlated or uncorrelated?
e) Let U= X-Y, V=X+Y find fU,V(u,v)
f) Find cov(U,V), are U and V positively correlated, negatively correlated or uncorrelated?