Suppose that X follows the Kumaraswamy distribution with pdf f(x) = 2ar (1– 1ª) on 0 0. (a) By integrating the pdf, show that the cdf, F(z), is given by F(x) = 1- (1- 1“)² on 0
Suppose that X follows the Kumaraswamy distribution with pdf f(x) = 2ar (1– 1ª) on 0 0. (a) By integrating the pdf, show that the cdf, F(z), is given by F(x) = 1- (1- 1“)² on 0
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Suppose that X follows the Kumaraswamy distribution with pdf
f(x) = 2ar (1– 1ª) on 0<I< 1,
where a > 0.
(a) By integrating the pdf, show that the cdf, F(z), is given by
F(x) =1- (1– 2ª“)² on 0<z<1.
%3D
Hint: You may find the substitution y = 1" useful.
(b) Show that the quantile function Q(a) is given by
= (1 – (1 – a)})*.
Q(a)
%3D
(c) If a = 1, find the probability that X lies between and.
(d) Again, for a = 1, show that the interquartile range of X is
V3 - 1
IQR =
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