Let x₁, x₂,, x₁₀ be ten observations such that Σ i=1 ¹⁰(x i -2)=30, Σ i=1 ¹⁰(x i -β)²=98, β>2, and their variance is 4/5. If μ and σ² are respectively the mean and the variance of 2(x₁-1)+4β, 2(x₂-1)+4β,, 2(x₁₀-1)+4β, then (β μ)/(σ²) is equal to:

Statistics and Probability: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q101

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumStatistics and Probability258× since 2002

Let

x_1, x_2, \ldots, x_{10}

be ten observations such that

\sum_{i=1}^{10}(x_i-2)=30

\sum_{i=1}^{10}(x_i-\beta)^2=98

\beta>2

, and their variance is

\frac{4}{5}

. If

\mu

and

\sigma^2

are respectively the mean and the variance of

2(x_1-1)+4\beta

2(x_2-1)+4\beta

\ldots

2(x_{10}-1)+4\beta

, then

\frac{\beta \mu}{\sigma^2}

is equal to: