b) Let X₁, X2, ..., X and Y₁, Y2, ..., Ym be random samples from populations with moment generating 25 functions Mx, (t) = e3t+t² and My (t) = (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(|Y-µ| ≥10) < 0.04?
b) Let X₁, X2, ..., X and Y₁, Y2, ..., Ym be random samples from populations with moment generating 25 functions Mx, (t) = e3t+t² and My (t) = (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(|Y-µ| ≥10) < 0.04?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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![b)
Let X₁, X₂, ..., Xn and Y₁, Y2,..., Ym be random samples from populations with moment generating
25
functions Mx, (t) = e3t+t² and My₁ (t) =
(₁
(₁), respectively.
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[₁(X₁-X)² > 68.3392] = 0.025?
iii) What is the value of the sample size m, if P(|Y-My ≥10) < 0.04?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd589ba33-46f0-43e1-9ef3-a17990fe3dce%2F51888632-7665-4fde-9ba0-0462c480b6f4%2Fqqgfp85_processed.jpeg&w=3840&q=75)
Transcribed Image Text:b)
Let X₁, X₂, ..., Xn and Y₁, Y2,..., Ym be random samples from populations with moment generating
25
functions Mx, (t) = e3t+t² and My₁ (t) =
(₁
(₁), respectively.
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[₁(X₁-X)² > 68.3392] = 0.025?
iii) What is the value of the sample size m, if P(|Y-My ≥10) < 0.04?
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