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

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Question

(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

Vedclass · Accepted Answer

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

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}$

	Physics	Chemistry	Mathematics	Biology
Mean	$20$	$25$	$23$	$27$
$S$.$D$.	$3$	$2$	$4$	$5$

Classes	$0-30$	$30-60$	$60-90$	$90-120$	$120-150$	$150-180$	$180-210$
$f_i$	$2$	$3$	$5$	$10$	$3$	$5$	$2$

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

Similar Questions

The following table shows the information about marks obtained in Physics,Chemistry,Mathematics,and Biology by $100$ students in a class. Which subject shows the highest variability in marks?
Physics Chemistry Mathematics Biology
Mean $20$ $25$ $23$ $27$
$S$.$D$. $3$ $2$ $4$ $5$

Find the mean and variance for the following frequency distribution:

Classes $0-30$ $30-60$ $60-90$ $90-120$ $120-150$ $150-180$ $180-210$

$f_i$ $2$ $3$ $5$ $10$ $3$ $5$ $2$

Find the variance of the first $20$ natural numbers.

The sum of $10$ values is $12$ and the sum of their squares is $16.9$,then their standard deviation $(S.D.)$ is

The mean of $5$ observations is $15$ and variance is $9$. If two observations having values $-5$ and $13$ are combined with these observations,then what will be the new variance?

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