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Show that overset(n)underset(i=1)sum (xi...

Show that `overset(n)underset(i=1)sum (x_i - A)^2` is minimum when `A = barx`.

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Prove that 1/n overset(n)underset(E_1)sum |x_i - A| attains, minimum when A = Median.

Find the value of overset(10)underset(i=1)sum(10xxi) .

A variable assumes the values x_1 , x_2 ,…….., x^_n with frequencies f_1 , f_2 ,………, f_n In respectively, show that overset(n)underset(i=1)sum f_i(x_i - barx) = 0 .

If x_1 , x_2 ,……. x_n are real quantities. Prove that 1/n overset(n)underset(i=1)sum x i^2 ge (1/n overset(n)underset(i=1)sum|x i|)^2

Show that: overset(1)underset(0)int (log(1+x)/(1+x^2))dx= pi/8 log 2 .

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Let f(1)=1 and f(n)=2overset(n-1)underset(r=1)sum f( r ) . Then overset(m) underset(n=1)sum f(n) is equal to

Let x be a variable assuming the values 1, 2,……….k and let F_1 = n , F_2 ,…… F_k be the corresponding cumulative frequencies of the greater than type show that barx = 1/n overset(k)underset(i=1)sum F_i .

UNITED BOOK HOUSE-Hare School, Question Paper -Exercise
  1. If P(A) = 1/2, P(B) = 2/3 then prove that 1/6 le P(A nn B) le 1/2

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  2. If 9 biscuits of different types be distributed among 3 children, find...

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  3. Show that overset(n)underset(i=1)sum (xi - A)^2 is minimum when A = ba...

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  4. If y = (x-a)/b, then prove that Sy = frac(Sx)(|b|)

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  5. Prove that P(A uu B) = P(A) + P(B) - P(A nn B)

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  6. The variance of 1, 2,…………..n is 24. Find n.

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  7. For 10 values of X, it is given that sumu = 4 and sum u^2 = 144, where...

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  8. Two groups of 15 and 22 values have variances 9 and 16 respectively. I...

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  9. For a set of an positive quantities prove that AM ge GM ge HM.

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  10. Prove that 1/n overset(n)underset(E1)sum |xi - A| attains, minimum whe...

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  11. Let x be a variable assuming the values 1, 2,……….k and let F1 = n, F2,...

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  12. |x-2| le 6 implies that

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  13. When it comes to comparing different segments among themselves and als...

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  14. Mode of a distribution can be obtained from

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  15. Frequency curve is the limiting form of

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  16. If the AM and HM of two numbers are 16 and 4 respectively, then the GM...

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  17. If the median and mode for a moderate asymmetrical distribution are 8 ...

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  18. If 2x + 3y = 6 and S.D. of X = 6, the S.D. of y is -

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  19. If the C.V. is 40 and SX^2 = 400, then barx is

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  20. If 3x - 2y + 6 = 0, R(x) = 4, then R(y) is

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