Let me start off by saying that I AM NOT ASKING YOU TO DO MY HOMEWORK FOR ME. Too often when I post questions like this people don't answer the question and tell me to do my own homework. I am not asking you to do it for me, I am asking you to help show me how it is done because I don't understand. So here is the problem I am struggling with:
Three patients are enrolled in a clinical trial. Each patient either has a complete response to initial treatment or not. The probability of a complete response for any patient is 0.6 and the response of each patient is independent of the others. Let X denote the number of complete responders out of the first two patients enrolled. Let Y denote the number of complete responders out of the second and third patients enrolled.
a) Find the conditional distribution of Y given X=1.
b) Find cov(X,Y).
I know how to find a conditional distribution and covariance in a general case, but I don't know what to do in this case. How do I set this problem up? Is the joint distribution multinomial, like so:
Or is it something else? I honestly don't know. Anyone give me a pointer?