Let X11, X12,..., Xin, and X21, X22, X2n₂ be two independent random samplesof size n₁ and n₂ from two normal populations N(₁, 0) and N(2, 2) respectively.n₂Let X₂Xij, S² =Σ(Xij- Xi)² for i=1,2.j=1n₂j=1ni -(a) Using an appropriate statistic and a parameter from the above specifications,define a function/quantity that follows a chi-square distribution with (n₁ - 1)degrees of freedom.(b) Argue that the above chi-square statistic is a pivotal quantity and can beused to define a (1-a) x 100% confidence interval for the relevant populationvariance. Derive the confidence interval for the population variance, clearlystating its limits.

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Answered: Let X11, X12, Xin, and X21, X22, X2n₂…

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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