Example 9-49. For the exponential distribution f(x) = e-x, x 2 0; show that the cumulative distribution function (c.d.f.) of X(n) in a random sample of size n is : F, (x) = (1 – e-x)n. Hence prove that as n → o, the c.d.f. of X(n) – log n tends to the limiting form exp [-{exp (– x)}] – ∞< x < o.
Example 9-49. For the exponential distribution f(x) = e-x, x 2 0; show that the cumulative distribution function (c.d.f.) of X(n) in a random sample of size n is : F, (x) = (1 – e-x)n. Hence prove that as n → o, the c.d.f. of X(n) – log n tends to the limiting form exp [-{exp (– x)}] – ∞< x < o.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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