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Probability and Statistics for Engineering
Homework 3
Spring 2011
(due Tuesday, February 8)
(1)
Suppose
is a discrete random variable with
and
.
(Let's just say
\
œ $!
œ %
\
.5
\\
represents some type of count.)
(a) Find
.
IÒ "!! #\Ó
(b) Find Var
.
Ð"!! #\Ñ
(c) Find
.
5
"!!#\
(d)
Write a Chebyshev statement with
for
(in words, not symbols).
5œ&
\
(2)
Recall the roulette wheel random variable
from Homework 2.
]Ð
]
counts the number of
spins needed until the ball lands in a black slot.
Ñ
The density table is as follows.
12
3
4
Cá
0ÐCÑ
*"
!
!*"
!*
"*
"*
"*
"*
"*
"*
"*
†††
Š‹
#
3
It is surprisingly difficult to find the mean of
.
(If you apply the expected value formula
]
directly, you end up with an infinite sum which is not a geometric series.
Try it if you like.)
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This document was uploaded on 05/15/2011.
 Spring '09

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