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Probability and Statistics for Engineering
Homework 5
Spring 2011
(due Tuesday, March 1)
(1) Completely simplify the value
.
(Keep it exact rather than getting a decimal
/
#
$
ln
approximation for it.)
This should prove to be useful below.
(2)
Consider the following function
, which is a density function for a continuous random
0
variable .
\
0ÐBÑ œ /
! Ÿ B Ÿ
$
*
%
#B
ln
(a)
Find the mean of
directly (via integration, using the definition of the mean).
Show
\
all your work, including the details of the integration.
Give your answer
in exact
both
form (in terms of logarithms and/or exponentials, completely simplified)
as a
and
decimal, rounded to four decimal places.
(b)
Find the moment generating function for
.
Show your work.
There won't be much
\
simplifying you can do at the end, and that's OK.
(c)
Find the mean of
using the moment generating function.
Show your work.
\
Hint 1
.
Of course, your answers for (a) and (c) should match.
If they are not the same,
don't change something randomly to force them to match.
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This document was uploaded on 05/15/2011.
 Spring '09

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