I'm a bit confused with this question. So the equation is Y=aX+Ei where:

a: can be positive integer

X: 1-20.

Ei: Uniform distribution of integers from [-9, 9].

It goes on to ask, show and discuss the theoretical distribution of Y|X and Ei.

Well, wouldn't the theoretical distribution of Ei be uniformed? I'm not sure how am I suppose to show it? I'm not sure what the theoretical distribution of Y|X would be. From what the professor said, it should be uniformed too, but that doesn't really make any sense. It would make sense if x was uniformly distributed too, but x is just integers from 1-20.

Thanks for your help!