2. Let Xn have distribution function sin(2nxx) 2nπ Fn(x)=x− 0≤x≤1. (a) Show that Fn is indeed a distribution function, and that Xn has a density function. (b) Show that, as noo, Fn converges to the uniform distribution function, but that the density function of Fn does not converge to the uniform density function. 3

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.CR: Chapter 13 Review
Problem 52CR
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2.
Let Xn have distribution function
CH
sin(2nxx)
2nπ
Fn(x)=x−
(a) Show that Fn is indeed a distribution function, and that Xn has a density function.
(b) Show that, as noo, Fn converges to the uniform distribution function, but that the density
function of Fn does not converge to the uniform density function.
0≤x≤1.
3
Transcribed Image Text:2. Let Xn have distribution function CH sin(2nxx) 2nπ Fn(x)=x− (a) Show that Fn is indeed a distribution function, and that Xn has a density function. (b) Show that, as noo, Fn converges to the uniform distribution function, but that the density function of Fn does not converge to the uniform density function. 0≤x≤1. 3
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