(c) In 1955, C.W. Topp and F.C. Leone introduced a number of distributions in the context of the statistical modelling of the reliability of electronic components in engineering. One of these distributions has probability density function (p.d.f.) given by f(x) = 4x(1x) (2 - x) on the range 0 < x < 1. (i) Verify, by integration, that [ 4x(1 − x)(2 − x) dx : 4x(1-x)(2-x) dx = x²(2 − x)² + c, where c is an arbitrary constant. (ii) Explain why the p.d.f. suggested by Topp and Leone is a valid p.d.f. (iii) What is the c.d.f. associated with this p.d.f.?
(c) In 1955, C.W. Topp and F.C. Leone introduced a number of distributions in the context of the statistical modelling of the reliability of electronic components in engineering. One of these distributions has probability density function (p.d.f.) given by f(x) = 4x(1x) (2 - x) on the range 0 < x < 1. (i) Verify, by integration, that [ 4x(1 − x)(2 − x) dx : 4x(1-x)(2-x) dx = x²(2 − x)² + c, where c is an arbitrary constant. (ii) Explain why the p.d.f. suggested by Topp and Leone is a valid p.d.f. (iii) What is the c.d.f. associated with this p.d.f.?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:(c) In 1955, C.W. Topp and F.C. Leone introduced a number of
distributions in the context of the statistical modelling of the reliability
of electronic components in engineering. One of these distributions has
probability density function (p.d.f.) given by
f(x) = 4x(1x) (2x)
on the range 0<x< 1.
(i) Verify, by integration, that
| 4x(1 − x)(2 − x) dx = x²(2 − x)² + c,
-
where c is an arbitrary constant.
(ii) Explain why the p.d.f. suggested by Topp and Leone is a valid
p.d.f.
(iii) What is the c.d.f. associated with this p.d.f.?
(iv) Suppose that X is a random variable following this p.d.f., and that
we are interested in evaluating P( < X <3). Write this
probability in terms of the c.d.f., and hence show that
P ( 1/3 < X
(which is approximately 0.481).
39
81
X< =
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