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If the mean and variance of one set of values be `barx_1` and `s_1^2` and those of another set be `barx_2` and `s_2^2` respectively and each set has values 2, then prove that the variance `(s^2)` of the combined set of values is given by `4s^2 = 2(s_1^2 + s_2^2) + d^2` where `d = (barx_1 - barx_2)`.

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UNITED BOOK HOUSE-Nava Nalanda School, Question Paper -Exercise
  1. If Y = a + bx, a, b be two real constants, then prove that Range (y) =...

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  2. Prove that logn(n + 1) > log(n + 1) (n + 2), for n > 1.

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  3. Show that for any set of n real values x1, x2,…….xn. x1^2 + x2^2 + …....

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  4. State Remainder theorem.

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  5. If a, b, c are all positive, prove that 6abc le bc(b + c) + ca(c + a) ...

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  6. Find the degree two polynomial function f(x) for which it is known tha...

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  7. If a variable assumes n values a, ar,………ar^(n - 1) (r < 1) with equal ...

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  8. Write a short note on histogram of a frequency distribution.

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  9. Write down the merits and demerits of mass questionnaire method.

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  10. if sin^4x+sin^2x=1,then prove that cot^4x+cot^2x=1.

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

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  12. Write a general formula expressing central moments in terms of raw mom...

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  13. If s and R are respectively the standard deviation and range of set of...

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  14. If barx1 and barx2 are the A.M. of two sets with n1 and n1 observation...

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  15. Derive the formula of median from ogive for a frequency distribution.

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  16. Prove that all odd-ordered central moments are zero for a symmetrical ...

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  17. Derive Lagrange's interpolation formula.

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

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  19. If the mean and variance of one set of values be barx1 and s1^2 and th...

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  20. In a frequency table, the upper boundary of each class-interval has a ...

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