Let \(X\) have the discrete uniform on \(\{1,\,2,\,...,\,n\}\). This means \(P(X=i)=1/n\) for all \(i = 1,\,2,\,...,\,n\).

1. Compute the MGF of \(X\);
2. Use it to compute the mean;
3. Use it to compute the variance.