i) Find the sampling distribution of the statistic W = X₁ + 2X₂ − X3 + X₁ + X5. ii) What is the value of the sample size n, if P[Σï=₁(X₁ − X)² > 68.3392] = 0.025? iii) What is the value of the sample size m, if P(|Ỹ - μ| ≥ 10) < 0.04?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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b)
Let X₁, X₂, ..., Xn and Y₁, Y₂, ..., Ym be random samples from populations with moment generating
functions Mx₁(t) = ³t+t² and My(t) = (₁¹)²5, respectively.
i) Find the sampling distribution of the statistic W = X₁ + 2X₂ − X3 + X4 + X5.
ii) What is the value of the sample size n, if P[₁(X; - X)² > 68.3392] = 0.025?
iii) What is the value of the sample size m, if P(|Ỹ - µỹ| ≥ 10) < 0.04?
Transcribed Image Text:b) Let X₁, X₂, ..., Xn and Y₁, Y₂, ..., Ym be random samples from populations with moment generating functions Mx₁(t) = ³t+t² and My(t) = (₁¹)²5, respectively. i) Find the sampling distribution of the statistic W = X₁ + 2X₂ − X3 + X4 + X5. ii) What is the value of the sample size n, if P[₁(X; - X)² > 68.3392] = 0.025? iii) What is the value of the sample size m, if P(|Ỹ - µỹ| ≥ 10) < 0.04?
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