2.8 Consider the triangular random variable with pdf 0 if x < 2a or x > 2b, if 2a < x

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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2.8
Consider the triangular random variable with pdf
0
f(x) =
X
X
2a
(b − a)²
(2b − x)
(b − a)²
if x < 2a or x > 2b,
if 2a < x <a+b,
if a + b < x < 2b.
a) Derive the corresponding cdf F.
b) Show that applying the inverse-transform method yields
2a + (b-a)√2U
2b + (a − b) √2(1 – U)
if 0 <U</,
if <U < 1.
Transcribed Image Text:2.8 Consider the triangular random variable with pdf 0 f(x) = X X 2a (b − a)² (2b − x) (b − a)² if x < 2a or x > 2b, if 2a < x <a+b, if a + b < x < 2b. a) Derive the corresponding cdf F. b) Show that applying the inverse-transform method yields 2a + (b-a)√2U 2b + (a − b) √2(1 – U) if 0 <U</, if <U < 1.
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