Consider two independent random samples x_(1),x_(2),dots,x_(n) and Y_(1),Y_(2),dots,Y_(n) taken from \Gamma (k,\lambda _(1)) and \Gamma (k,\lambda _(2)), re- spectively, where \lambda _(1) and \lambda _(2) are the scale parameters for the dis- tributions. Assume that k is known. Show that the lower and upper limits of the confidence interval of (\lambda _(1))\ (\lambda _(2)) interval can be expressed as functions of the quantiles of the F distribution.

Consider two independent random samples x_(1),x_(2),dots,x_(n) and Y_(1),Y_(2),dots,Y_(n) taken from \Gamma (k,\lambda _(1)) and \Gamma (k,\lambda _(2)), re- spectively, where \lambda _(1) and \lambda _(2) are the scale parameters for the dis- tributions. Assume that k is known. Show that the lower and upper limits of the confidence interval of (\lambda _(1))\ (\lambda _(2)) interval can be expressed as functions of the quantiles of the F distribution.

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

Section13.3: Special Probability Density Functions

Problem 30E

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