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ECE 804, Random Signal Analysis
Nov. 10, 2008
OSU, Autumn 2008
Due: Nov. 17, 2008
Problem Set 7
Problem 1
We want to obtain the mold content per volume,
m
, of the water in the Dreese building,
with an error that, with 95 % probability, is less than 0
.
1. The technique we use for this
measurement has an error that is random with mean 0 and standard deviation 2. So, we
can model our measurements as
X
i
=
m
+
N
i
, where
N
i
is the noise in measurement
i
,
with a mean of 0, and a std. deviation of 2. The
N
i
’s are independent for
i
= 1
,
2
, . . .
.
In order to reduce the error, we perform a number of measurements and compute their
average:
M
n
=
1
n
n
X
i
=1
X
i
(a) Find the mean and the variance of
M
n
.
(b) Suppose we model
M
n
as a Gaussian random variable.
With this approximation,
what is the number of measurements needed to achieve the desired reliability?
(c) Using the Chebychev Inequality, ±nd an upper bound on the number of measurements
we need to achieve the reliability goal.
Problem 2
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