(a) Show that the conditional distribution function ofthe continuous random variable X, given a < X F b, isgiven by F(x|a < X F b) =⎧⎪⎪⎪⎨⎪⎪⎪⎩0 for x F aF(x) − F(a)F(b) − F(a) for a < x F b1 for x > b(b) Differentiate the result of part (a) with respect tox to find the conditional probability density of X givena < X F b, and show that E[u(X)|a < X F b] = bau(x)f(x) dx baf(x) dx
(a) Show that the conditional distribution function ofthe continuous random variable X, given a < X F b, isgiven by F(x|a < X F b) =⎧⎪⎪⎪⎨⎪⎪⎪⎩0 for x F aF(x) − F(a)F(b) − F(a) for a < x F b1 for x > b(b) Differentiate the result of part (a) with respect tox to find the conditional probability density of X givena < X F b, and show that E[u(X)|a < X F b] = bau(x)f(x) dx baf(x) dx
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
(a) Show that the conditional distribution function of
the continuous random variable X, given a < X F b, is
given by
the continuous random variable X, given a < X F b, is
given by
F(x|a < X F b) =
⎧
⎪⎪⎪⎨
⎪⎪⎪⎩
0 for x F a
F(x) − F(a)
F(b) − F(a)
⎧
⎪⎪⎪⎨
⎪⎪⎪⎩
0 for x F a
F(x) − F(a)
F(b) − F(a)
for a < x F b
1 for x > b
(b) Differentiate the result of part (a) with respect to
x to find the conditional probability density of X given
a < X F b, and show that
1 for x > b
(b) Differentiate the result of part (a) with respect to
x to find the conditional probability density of X given
a < X F b, and show that
E[u(X)|a < X F b] =
b
a
u(x)f(x) dx
b
a
f(x) dx
b
a
u(x)f(x) dx
b
a
f(x) dx
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