Let the observation x _ i (1 ≤ i ≤ 10) satisfy the equations ∑ _ i = 1 ^ 10 ( x _ i - 5) = 10 , ∑ _ i = 1 ^ 10 ( x _ i - 5) ^ 2 = 40 . If μ and λ are the mean and the variance of the observations, x _ 1 - 3, x _ 2 - 3

Correct answer: A. (3,3) Mean ( x _ i - 5) = ∑ ( x _ i - 5) 10 = 1 ∴ \ Mean( x _ i - 5)\ + 2 = 3 μ = var( x _ i - 5) = ∑ ( x _ i - 5) ^ 2 10 - ∑ ( x _ i - 5) 10 = 3

JEE Main 20209 JanuaryMorning Shift

Exam: JEE Main
Year: 2020
Date: 9 January
Shift: Morning Shift
Subject: Mathematics
Chapter: Statistics

JEE Main 2020 · 9 January · Morning Shift · Mathematics · Statistics

Let the observation x _ i (1 ≤ i ≤ 10) satisfy the equations ∑ _ i...

Let the observation

{x}_{i}\left(1 \le i \le 10\right) satisfy

the equations\mathop{∑}_{i = 1}^{10}\left({x}_{i} - 5\right)

= 10

\mathop{∑}_{i = 1}^{10}{\left({x}_{i} - 5\right)}

^{2} = 40

. If

\mu

and

\lambda

are the mean and the variance of the observations,

{x}_{1} - 3, {x}_{2} - 3, . . . . , {x}_{10} - 3,then the

ordered pair \left(\mu, \lambda\right) is equal to:

Options

A $\left(3,3\right)$
B $\left(6,3\right)$
C $\left(6,6\right)$
D $\left(3,6\right)$

Correct answer

A. $\left(3,3\right)$

Step-by-step solution

Mean

\left({x}_{i} - 5\right) = \dfrac{∑ \left({x}_{i} - 5\right)}{10} = 1 ∴ \left\{Mean\left({x}_{i} - 5\right)\right\} + 2 = 3

\mu = var\left({x}_{i} - 5\right) = \dfrac{∑ {\left({x}_{i} - 5\right)}^{2}}{10} - \dfrac{∑ \left({x}_{i} - 5\right)}{10} = 3

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