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Let Xn have distribution function sin(2n+x) Fn(x) = x − 2nt 0 ≤ x ≤ 1. (a) Show that F is indeed a distribution function, and that X, has a density function. - (b) Show that, as n → ∞, F₁ converges to the uniform distribution function, but that the density function of Fn does not converge to the uniform density function.

Let Xn have distribution function sin(2n+x) Fn(x) = x − 2nt 0 ≤ x ≤ 1. (a) Show that F is indeed a distribution function, and that X, has a density function. - (b) Show that, as n → ∞, F₁ converges to the uniform distribution function, but that the density function of Fn does not converge to the uniform density function.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Exercise 5.9.2 from the book. Let Xn have distribution function Fn(x): = x- sin(2nлx) 2nл 0≤x≤ 1. (a) Show that Fn is indeed a distribution function, and that Xn has a density function. (b) Show that, as n → ∞, Fn converges to the uniform distribution function, but that the density function of Fn does not converge to the uniform density function.
Transcribed Image Text:Exercise 5.9.2 from the book. Let Xn have distribution function Fn(x): = x- sin(2nлx) 2nл 0≤x≤ 1. (a) Show that Fn is indeed a distribution function, and that Xn has a density function. (b) Show that, as n → ∞, Fn converges to the uniform distribution function, but that the density function of Fn does not converge to the uniform density function.
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