The variance of ^{10}C_0, ^{10}C_1, ^{10}C_2, | vedclass

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(D) The variance is given by $\sigma^2 = \frac{\sum_{i=0}^{10} x_i^2}{n} - \left(\frac{\sum_{i=0}^{10} x_i}{n}\right)^2$,where $n = 11$ is the number

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$\frac{11 \cdot ^{20}C_{10} - 2^{20}}{121}$

Vedclass · Answer

(D) The variance is given by $\sigma^2 = \frac{\sum_{i=0}^{10} x_i^2}{n} - \left(\frac{\sum_{i=0}^{10} x_i}{n}\right)^2$,where $n = 11$ is the number of observations.Here,$\sum_{i=0}^{10} {^{10}C_i} = 2^{10}$ and $\sum_{i=0}^{10} (^{10}C_i)^2 = ^{20}C_{10}$.Substituting these values into the formula:$\sigma^2 = \frac{^{20}C_{10}}{11} - \left(\frac{2^{10}}{11}\right)^2$$\sigma^2 = \frac{11 \cdot ^{20}C_{10} - (2^{10})^2}{121}$$\sigma^2 = \frac{11 \cdot ^{20}C_{10} - 2^{20}}{121}$

${x_i}$	$3$	$8$	$13$	$18$	$23$
${f_i}$	$7$	$10$	$15$	$10$	$6$

The variance of $^{10}C_0, ^{10}C_1, ^{10}C_2, \dots, ^{10}C_{10}$ is:

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