Let X1 and X2 be independent random variables that are unifo

Let X1 and X2 be independent random variables that are uniformly
distributed on {1,

Solution

since uniformly distributed

the pdf is : 1/n

given s=x₁+x₂ =

pmf(s) = pmf(x₁+x₂) =1/n

since x₁+x₂ is an integer hence the distribution is uniform it need to be same