So I have an assignment regarding probability that states the following:
Six terminals are connected in a communication line. Exactly 3 of the 6 terminals are functional and 3 are not. Each terminal has a fair chance of being picked of if we define the event A which states that we pick a functional terminal from the 6, then P(A)=0.5.
The terminals are being inspected in order until we find a functional terminal.
Let X be the random variable that defines the number of inspections we need to make until we find the first functional terminal, and Y be the random variable that defines the number of inspections we need to make until we find the second working terminal.
We need to find the law of distribution for the two-dimensional random variable {X,Y}.
I've managed to find the marginal distribution of both X and Y separately but I have no idea how to the distribution for the vector {X,Y}.
And ideas?