Here is a little probability problem I am trying to resolve. I am sure you can help.
Let's say there are two random variables X and Y. They are both binary random variables such as probability of Heads from a coin toss. Let the probabilities of heads be p1 and p2. Suppose I also know that these probabilities are positively correlated -- correlation coefficient R (standard definition of correlation --> covariance/(sigma(X)*sigma(Y)).
I want the probability of getting heads in both -- which is greater than p1*p2. Of course I can simulate this. But is there a formula that can tell me the probability or can it be derived?
Let's say there are two random variables X and Y. They are both binary random variables such as probability of Heads from a coin toss. Let the probabilities of heads be p1 and p2. Suppose I also know that these probabilities are positively correlated -- correlation coefficient R (standard definition of correlation --> covariance/(sigma(X)*sigma(Y)).
I want the probability of getting heads in both -- which is greater than p1*p2. Of course I can simulate this. But is there a formula that can tell me the probability or can it be derived?