The formula for finding P(X>4Y) given joint pdf is P(X>4Y) = ∫∫ p(x,y) dx dy, where p(x,y) is the joint probability density function.
The joint pdf represents the probability of both X and Y occurring simultaneously. It is a function that assigns a probability value to every point in the X-Y plane.
Yes, the joint pdf can be used to find other probabilities by integrating over the desired region in the X-Y plane. For example, to find P(X>4Y), we would integrate over the region where X>4Y.
The difference between P(X>4Y) and P(X,Y>4) is that the former represents the probability of X being greater than 4 times Y, while the latter represents the probability of both X and Y being greater than 4.
No, P(X>4Y) cannot be greater than 1 as it represents a probability and probabilities cannot exceed 1. It is possible for the integral to be greater than 1, but this would indicate an error in the calculation.