Prove. Let X₁, X₂,..., X be a r.s. from N(µ,σ²) and Y₁,Y,₂,...,Y, be another independent r.s. from N(μ₂,₂²). Then, (X-Ỹ)-(µ−μ₂) N(0,1). of 0232 + Vn₂ M₂ Some hints: (a) Use the remark about the distribution of X when the random sample comes from a normal distribution. No need to prove the remark. (b) Find the distribution of X - Y using the MGF technique.
Prove. Let X₁, X₂,..., X be a r.s. from N(µ,σ²) and Y₁,Y,₂,...,Y, be another independent r.s. from N(μ₂,₂²). Then, (X-Ỹ)-(µ−μ₂) N(0,1). of 0232 + Vn₂ M₂ Some hints: (a) Use the remark about the distribution of X when the random sample comes from a normal distribution. No need to prove the remark. (b) Find the distribution of X - Y using the MGF technique.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Transcribed Image Text:Prove.
Let X₁, X₂,..., X be a r.s. from N(µ,σ²) and Y₁,Y,₂,...,Y, be another independent r.s. from
N(μ₂,₂²). Then,
(X-Ỹ)-(µ−μ₂) N(0,1).
of 0232
+
Vn₂ M₂
Some hints:
(a) Use the remark about the distribution of X when the random sample comes from a normal
distribution. No need to prove the remark.
(b) Find the distribution of X - Y using the MGF technique.
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