Question

If a variable takes the values $0,1,2,...,n$ with corresponding frequencies as binomial coefficients ${}^n{C}_0,{}^n{C}_1,...,{}^n{C}_n$, then the mean of distribution is

• A. $\frac{\left(n\right)(n+1)}{4}$
• B. $\frac{n}{2}$
• C. $\frac{\left(n\right)(n-1)}{2}$
• D. $\frac{\left(n\right)(n+1)}{2}$

Answer 1

The correct option is B $\frac{n}{2}$

We know that $\text{mean}=\left(\frac{\sum f_i{x}_i}{\sum f_i}\right)$
Mean $=\frac{0.{}^n{C}_0+1.{}^n{C}_1+2.{}^n{C}_2+3.{}^n{C}_3+...+n.{}^n{C}_n}{{}^n{C}_0+{}^n{C}_1+...+{}^n{C}_n}$
= $\frac{n{.2}^{(n-1)}}{2^n}$
=$\frac{n}{2}$