The mean of the values 0, 1, 2,......,n having corresponding weight \[^{n}{{C}_{0}},{{\,}^{n}}{{C}_{1}},{{\,}^{n}}{{C}_{2}},........\,,{{\,}^{n}}{{C}_{n}}\] respectively is [AMU 1990; CET 1998]

• A.                 \[\frac{{{2}^{n}}}{n+1}\]        
• B.                 \[\frac{{{2}^{n+1}}}{n(n+1)}\]
• C.                 \[\frac{n+1}{2}\]    
• D.                 \[\frac{n}{2}\]