2. A six-sided die is rolled repeatedly. Let X denote the first score of 4 or
more and let Y denote the first score of 5 or more.
[For the sequence of rolls starting 4, 2, 6, 5, . . . we have X = 4, Y = 6; for the
sequence starting 6, 4, 3, . . . we have X = 6 = Y . ]
(a) Write down in a table the joint probability distribution of (X, Y ) and find the
marginal distributions of X and Y.
The Attempt at a Solution
Can do joint distributions but how to do for this where the number of rolls isn't specified?