Let X be the height of a man and Y be the height of his daughter(both in inches). Suppose that the joint probability density function of X and Y is bivariatenormal with the following parameters: mean of X=71, mean of Y=60, std. deviation of X=3, Std. deviation of Y=2.7, and p(rho)=.45.Find the probability that the man is at least 8 inches taller than his daughter.
The Attempt at a Solution
X=N(71,9); Y=N(60,7.29); X-Y=N(11,1.71)
The difficulty I am having here is determining when to apply the p(rho)=.45 factor.
Should I apply it to the .0110 probability, or do I apply it sometime earlier?
Assistance would be very much appreciated!