A) \[\frac{n+1}{2}\]
B) \[\frac{n-1}{2}\]
C) \[\frac{{{2}^{n}}-1}{2}\]
D) \[\frac{{{2}^{n}}+1}{2}\]
E) \[\frac{n}{2}\]
Correct Answer: E
Solution :
Mean \[=\frac{0{{\times }^{n}}{{C}_{0}}+1{{\times }^{n}}{{C}_{1}}+2{{\times }^{n}}{{C}_{2}}+...+n{{\times }^{n}}{{C}_{n}}}{^{n}{{C}_{0}}{{+}^{n}}{{C}_{1}}{{+}^{n}}{{C}_{2}}+...{{+}^{n}}{{C}_{n}}}\] \[=\frac{0+1{{\times }^{n}}{{C}_{1}}+2{{\times }^{n}}{{C}_{2}}+...+n{{\times }^{n}}{{C}_{n}}}{{{2}^{n}}}\] \[=\frac{n{{.2}^{n-1}}}{{{2}^{n}}}=\frac{n}{2}\]
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