A device is used in many kinds of systems. Assume that allsystems have either 1, 2, 3, or 4 of these devices and that each ofthese four possibilties is equally likely to be the case. Eachdevice in a system has probablility = 0.1 of failing, and thedevices function independently of one another. This implies thatonce we know how many devices are present, the probabilitydistribution of the number of failures will be known. E.g. if asystem employs 3 of the devices, then the number that fail willhave a binomial distribution with parameters n = 3 and p =0.1
Denote with X, the number of failures of devices in the system, andwith Y, the total number of devices in the system. What is observedis that for b = 1,2,3, and 4, the conditional probability massfunction is the binomial probability mass function with parametersn = b, and p = 0.1
a) Find the joint probability mass table of P(X,Y)
