Consider an experiment that consists of 2 rolls of a balanced die. If X is the number of 4s and Y is the number of 5s obtained in the 2 rolls of the die, find the joint probability function. because there are ways to combine x 4s and ways to combine y 5s, and 36 possible combinations from a throw with 2 dice. However, this formula doesn't give me the correct probability distribution of X and Y. What's my mistake?
I can't follow what you are saying. What is Cx and Cy? The only nonzero values of the joint prob function will occur for the following cases: x=0, y=0 x=0, y=1 x=1, y=0 x=1, y=1 x=0, y=2 x=2, y=0 Note that x or y can be 0, 1 or 2 but x and y can not both be 2. You should be able to calculate the probability of each case, noting that the sum of all probablities should add to 1.