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
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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Question
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F804e05f0-47cc-4057-90bd-5b8178a84ad5%2Fd6ff6b88-a681-41ed-812d-c75a47d9bc49%2Fpsoz71o_processed.jpeg&w=3840&q=75)
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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