Random Seed Utilization

Imagine you have a function that generates a random integer between a specified minimum value, N, and a maximum value, M. Let's refer to this function as X. Now, take the output from this random integer generator and use it as the maximum value for another random function, while keeping the same minimum value N. This second function will be called Y. How would the distribution of the samples from function Y appear? Additionally, what would the expected value of these samples be?