Let be a random variable that follows a Poisson distribution, so that for some constant α its PMF is
![](https://test.transtutors.com/qimg/ee8e0137-0d13-4082-9127-3aa455fca47e.png)
Let be another random variable that, given M =m , is equally likely to take on any value in the set ![](https://test.transtutors.com/qimg/f43df01e-d2fa-4621-8693-8df2fbf1ab00.png)
(a) Find the joint PMF of M and N
(b) Find the marginal PMF of ![](https://test.transtutors.com/qimg/c0f749df-7e2c-474b-8824-e887d9125e19.png)