TS ICET 24 May 2018 Shift 1 Paper

Question : 144 of 200

Marks: +1, -0

The variance o f the following distribution is

\table\ \x_1:, 1,2,3,4,5,6,7,8,9,10;f(x_1):,1,2,3,4,5,6,7,8,9,10

Solution:

x	f(x)	xf(xi)	$\x^2$ f(xi)
1	1	$1^2$	$1^3$
2	2	$2^2$	$2^3$
3	3	$3^2$	$3^3$
4	4	$4^2$	$4^3$
5	5	$5^2$	$5^3$
.	.	.	.
.	.	.	.
.	.	.	.
10	10	$10^2$	$10^3$

Variance

=\;{∑ x_{i}^{2} f(x_{i})}/{∑ f(x_{i})}-({∑(x_{i} f(x_{i}))}/{∑ f x_{i}})^{2}

={1^{3}+2^{3}+⋅s+10^{3}}/{1+2+3+. . .+10}-({1^{2}+2^{2}+. . .+10^{2}}/{1+2+3+. . .+10})^{2}

=\;{10^{2}(11)^{2}}/{4} × \;{2}/{(10)(11)}-(\;{(10)(11)(21)}/{6 \;{(10.11)}/{2}})^{2}

=55-49=6

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