If X and Y are random variables such that E(X) = 10 , V(X) = 25 and E(Y) = 0 , V(Y) = 1 , the values of a, b such that Y = aX - b will be: - Mathematics MCQ Mathematics Mock Test - 9 2026 | ExamTest.live

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If X and Y are random variables such that E (X) = 10, V (X) = 25 and E (Y) = 0, V (Y) = 1, the values of a, b such that Y = a X - b will be:

Solution & Step-by-step Explanation

Given Y = a X - b . E (Y) = a E (X) - b 0 = a (10) - b ⟹ b = 10 a . V (Y) = V (a X - b) = a^{2} V (X) 1 = a^{2} (25) ⟹ a^{2} = 1/25 ⟹ a = \pm 1/5 .If a = 1/5, b = 10 (1/5) = 2 .If a = - 1/5, b = 10 (- 1/5) = - 2 .Thus (a, b) = (\pm 1/5, \pm 2) .

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If X and Y are random variables such that E (X) = 10, V (X) = 25 and E (Y) = 0, V (Y) = 1, the values of a, b such that Y = a X - b will be:

(- 1/5, - 2)

(\pm 1/5, \pm 2)

(1/5, 2)

None

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