Part CCSIR NET June 2025the-sum-from-3-to-10-has-eight-terms-so-the-t-has-8-degrees-of-freedom

The sum from 3 to 10 has eight terms so the t has 8 degrees of freedom

Let $(X_{1}, Y_{1}), (X_{2}, Y_{2}), \dots, (X_{10}, Y_{10})$ be a random sample from a bivariate normal distribution BVN $(μ_{1}, μ_{2}, σ_{1}^{2}, σ_{2}^{2}, ρ)$ with $μ_{1} = 5, μ_{2} = 6, σ_{1}^{2} = 4, σ_{2}^{2} = 9$ and $ρ = 1/2$ . Then, which of the following statements are true?

A.The distribution of $(1/ 7) \sum_{i}$ ₌ $_{1}^{10} (X_{i} - Y_{i} + 1)$ is N(0, 10)✓
B.The distribution of $(1/19) \sum_{i}$ ₌ $_{1}^{10} (X_{i} + Y_{i} - 11)^{2}$ is $χ^{2} -$ distribution with degrees of freedom 10✓
C.The distribution of $22 (X_{1} - 5) /\sqrt (\sum_{i}$ ₌ $_{3}^{10} (X_{i} - 5)^{2})$ is t-distribution with degrees of freedom 9
D.The distribution of $2 \sum_{i}$ ₌ $_{1}^{3} (Y_{i} - 6)^{2} / \sum_{i}$ ₌ $_{4}^{9} (Y_{i} - 6)^{2}$ is F-distribution with degrees of freedom 3 and 6.✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests boundary and endpoint.

See pricing

50 are analysed free — try those first.

The trap it tests

Boundary and endpoint

The statement turns at the edge of the interval, the domain, or the parameter range.

Drill statements like this

The sum from 3 to 10 has eight terms so the t has 8 degrees of freedom

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