Question

A variable takes the values of $0,1,2,......n$ with frequencies proportional to the binomial coefficients ${}^n{C}_0{,}^n{C}_1,......{,}^n{C}_{n+}$ , then mean of the distribution is

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

Answer 1

Answer: (B)

$\frac{n}{2}$

Mean, $\overline{x}=\frac{\sum x_i{f}_i}{\sum f_i}$ where, $x_i$ are the values and $f_i$ are their respective frequencies.

ie, $\overline{x}=\frac{{\sum }_{r=0}^{n}r{}^n{C}_r}{{\sum }_{r=0}^n{}^n{C}_r}=\frac{n{2}^{n-1}}{2^n}=\frac{n}{2}$

So, Option B is the correct answer.