Problem 6 (a) Let X-N(μ1,02) and Y-N(μ2,02) be independent, where μ2> μ₁>0. Show that Y-X- Ν(μ2 -11,262). (b) Let X₁,..., X and Y₁,...,Yn be i.i.d. copies of X and Y. Using the variables Z₁ = Y₁ - X₁, construct a (1-a)-confidence interval [an, bn] for μ₂-μ₁. (c) Take [an, bn] from part (b). Recall that μ₂>₁>0. Show that P{0 € [an, bn]}-0 (n →∞o).
Problem 6 (a) Let X-N(μ1,02) and Y-N(μ2,02) be independent, where μ2> μ₁>0. Show that Y-X- Ν(μ2 -11,262). (b) Let X₁,..., X and Y₁,...,Yn be i.i.d. copies of X and Y. Using the variables Z₁ = Y₁ - X₁, construct a (1-a)-confidence interval [an, bn] for μ₂-μ₁. (c) Take [an, bn] from part (b). Recall that μ₂>₁>0. Show that P{0 € [an, bn]}-0 (n →∞o).
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![Problem 6
(a) Let X-N(μ1,02) and Y-N(μ2,02) be independent, where μ2> μ₁>0. Show that Y-X -
Ν(μ2 - 11,207).
(b) Let X₁,..., X and Y₁,..., Yn be i.i.d. copies of X and Y. Using the variables Z₁ = Y; - Xi,
construct a (1-a)-confidence interval [an, bn] for μ2-μ1.
(c) Take [an, bn] from part (b). Recall that ₂ >₁ > 0. Show that
P{0 € [an, bn]} → 0
(n →∞o).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4575c695-56bc-4a6a-843f-ec886ca258f2%2Ff411dcba-9370-4d97-9b0b-9f5c32050289%2Fsaa5hdr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 6
(a) Let X-N(μ1,02) and Y-N(μ2,02) be independent, where μ2> μ₁>0. Show that Y-X -
Ν(μ2 - 11,207).
(b) Let X₁,..., X and Y₁,..., Yn be i.i.d. copies of X and Y. Using the variables Z₁ = Y; - Xi,
construct a (1-a)-confidence interval [an, bn] for μ2-μ1.
(c) Take [an, bn] from part (b). Recall that ₂ >₁ > 0. Show that
P{0 € [an, bn]} → 0
(n →∞o).
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