Let X be a uniform RV U(a, b) with CDF {0 a (r-a)/(b a) a

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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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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Show that Y has a CDF that is U(a,b).

Let X be a uniform RV U(a, b) with CDF
{0
a
(r-a)/(b a) a <x <b
F(x)
for a <b
(a) Sketch the PDF of this distribution
(b) Let Z be a standard uniform random variable U(0, 1) and let Y be the
RV
Y =(b a)Z a.
Show that Y has a CDF that is U(a,b).
This means that a general uniform RV is just a linear transformation of
the standard one in the obvious way
Transcribed Image Text:Let X be a uniform RV U(a, b) with CDF {0 a (r-a)/(b a) a <x <b F(x) for a <b (a) Sketch the PDF of this distribution (b) Let Z be a standard uniform random variable U(0, 1) and let Y be the RV Y =(b a)Z a. Show that Y has a CDF that is U(a,b). This means that a general uniform RV is just a linear transformation of the standard one in the obvious way
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