Originally Posted by
braddy
problem 2:
A traffic engineer is studying the number of vehicles that arrive, during a certain 2-minute period, at two streets corners that are close to each other. Let X be the number of vehicles at on street corner and Y the number at the other. The enginner knows the joint distribution probability distribution of X and Y is:
-f(x,y)=(9/16)*(1/4)^(x+y), x=0,1,2,3..., y=0,1,2,....
- 0 elsewhere
For example P(X=1,Y=1)=0.035.
The enginner calculated E(X)=E(Y)=1/3, and Var(X)=Var(Y)=4/9.
He has calculated that X and Y are independent.