Variance of ^ 10 C_0 , ^ 10 C_1 , ^ 10 C_2 ,.... ^ 10 C_ 10 is - Vidyadip

MCQ

Variance of $^{10}C_0$ , $^{10}C_1$ , $^{10}C_2$ ,.... $^{10}C_{10}$ is

A
$\frac{{10.\,{}^{20}{C_{_{10}}} - {2^{10}}}}{{100}}$
B
$\frac{{11\,{}^{20}{C_{_{10}}} - {2^{10}}}}{{11}}$
C
$\frac{{10.\,{}^{20}{C_{_{10}}} - {2^{20}}}}{{100}}$
✓
$\frac{{11.\,{}^{20}{C_{_{10}}} - {2^{20}}}}{{121}}$

✓

Answer

Correct option: D.

$\frac{{11.\,{}^{20}{C_{_{10}}} - {2^{20}}}}{{121}}$

d
Variance $=\frac{\Sigma \mathrm{x}_{\mathrm{i}}^{2}}{\mathrm{n}}-\left(\frac{\Sigma \mathrm{x}_{\mathrm{i}}}{\mathrm{n}}\right)^{2}$

$=\frac{^{20} \mathrm{C}_{10}}{11}-\left(\frac{2^{10}}{11}\right)^{2}$

$=\frac{11 \cdot^{20} \mathrm{C}_{10}-2^{20}}{121}$

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