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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 0 and Y = ²₁X₁ i) Show that y follows a chi-square distribution with 2n degrees of freedom.

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 0 and Y = ²₁X₁ i) Show that y follows a chi-square distribution with 2n degrees of freedom.

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 19E
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9.STATISTICAL INFERENCE
Question 1 a i)

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 = 2 Sn ²i=1 X₁. i) Show that y follows a chi-square distribution with 2n degrees of freedom.
Transcribed Image Text: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 = 2 Sn ²i=1 X₁. i) Show that y follows a chi-square distribution with 2n degrees of freedom.
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