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a) Let X₁, X2, X3,..., X, be a random sample of size n from population X. Suppose that X follows an exponential distribution with parameter and Y = ²₁X₁. 84i=14 iv) Use the Central Limit Theorem to compute P(100

a) Let X₁, X2, X3,..., X, be a random sample of size n from population X. Suppose that X follows an exponential distribution with parameter and Y = ²₁X₁. 84i=14 iv) Use the Central Limit Theorem to compute P(100

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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a) Let X₁, X₂, X3,..., Xn be a random sample of size n from population X. Suppose that X follows an exponential distribution with parameter 0 and Y = = =1X₁. b) iv) Use the Central Limit Theorem to compute P(100 < Y < 115), for n = 40. Let X₁, X2, ..., X5 be a random sample of size 5 from the standard normally population. If the statistic Y is given by Y = X₁-X₂-X3 X₁²+X3²+X5² i) Briefly explain why Y follows a Student's t distribution with 3 degrees of freedom. ii) Compute the probability that Y is between 2.35 and 5.84. iii) What is the mean and variance of the statistic Y?
Transcribed Image Text:a) Let X₁, X₂, X3,..., Xn be a random sample of size n from population X. Suppose that X follows an exponential distribution with parameter 0 and Y = = =1X₁. b) iv) Use the Central Limit Theorem to compute P(100 < Y < 115), for n = 40. Let X₁, X2, ..., X5 be a random sample of size 5 from the standard normally population. If the statistic Y is given by Y = X₁-X₂-X3 X₁²+X3²+X5² i) Briefly explain why Y follows a Student's t distribution with 3 degrees of freedom. ii) Compute the probability that Y is between 2.35 and 5.84. iii) What is the mean and variance of the statistic Y?
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