by changing the indice, this is
X has uniform dist (0,1).
I found the MGF to be:
Now I need to expand the MGF in powers of s up to and use this to find the mean and variance of X. I know the series expansion for , but I'm not sure how to apply this in this situation.
EDIT: I think I understand what you did there.
But, I'm still stuck on another part of this question:
In adding n real numbers, each is rounded to the nearest integer. Assume that the round-off errors, , i = 1,...,n, are independently distributed as U(-0.5,+0.5). What is the approximate distribution of the total error, , in the sum of the n numbers?
How would I approach this question?