X follows U[0,1]
Y follows discrete uniform {0,1,..,n-1}
Z=X+Y.
distribution of Z?
Are they independent ?
If so, let k be an positive integer. Consider a z in . Let z=x+y, where x is the decimal part of z, and y its integer part.
So the probability that Z is in [k,k+1)=1/n (letting x=1)
So
This is the cdf of a uniform distribution over