$T h e a r i t h m e t i c m e a n o f t h e s e r i e s^{n} c_{0},^{n} c_{1},^{n} c_{2} . . . . .,^{n} c_{n} i s :$

\frac{2^{n}}{n + 1}

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\frac{2^{n}}{n}

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\frac{2^{n} - 1}{n + 1}

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none of these

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Solution

The correct option is A $\frac{2^{n}}{n + 1}$
$w e h a v e \sum x =^{n} C_{0} +^{n} C_{1} + . . . . . . +^{n} C_{0} = 2^{n} N o t e t h a t n u m b e r o f o b s e r v a t i o n s i s n + 1 ∴ ¯ x = \frac{2^{n}}{n + 1}$

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Similar questions

Q. The arithmetic mean of

^{n} C_{0},^{n} C_{1},^{n} C_{2}, . . .,^{n} C_{n}

T h e a r i t h m e t i c m e a n o f t h e s e r i e s^{n} c_{0},^{n} c_{1},^{n} c_{2} . . . . .,^{n} c_{n} i s :

Q. The arithmetic mean of the following frequency distribution:

Variable (X):	0	1	2	3	...	n
Frequency (f):	$^{n} C_{0}$	$^{n} C_{1}$	$^{n} C_{2}$	$^{n} C_{3}$	...	$^{n} C_{n}$

Q. The sum of the series

{10.}^{n} C_{0} + 10^{2} .^{n} C_{1} + 10^{3} .^{n} C_{2} + . . {.10}^{n + 1} .^{n} C_{n}

Let $S_{1}$ = $^{n} C_{0}$ + $^{n} C_{1}$ + $^{n} C_{2}$ ............. $^{n} C_{n}$ and $S_{2}$ = $^{n} C_{0}$ - $^{n} C_{1}$ + $^{n} C_{2}$ ..............+ $(- 1)^{n}$ $^{n} C_{n}$

Find the value of $\frac{S_{1}}{S_{1} + S_{2}}$ is ___.

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The arithmetic mean of the series nc0,nc1,nc2.....,ncn is:

The correct option is A 2nn+1wehave∑x=nC0+nC1+......+nC0=2nNote that number of observations is n+1∴ ¯x=2nn+1

$T h e a r i t h m e t i c m e a n o f t h e s e r i e s^{n} c_{0},^{n} c_{1},^{n} c_{2} . . . . .,^{n} c_{n} i s :$

The correct option is A $\frac{2^{n}}{n + 1}$
$w e h a v e \sum x =^{n} C_{0} +^{n} C_{1} + . . . . . . +^{n} C_{0} = 2^{n} N o t e t h a t n u m b e r o f o b s e r v a t i o n s i s n + 1 ∴ ¯ x = \frac{2^{n}}{n + 1}$