MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Civil and Environmental Engineering
1.017/1.010 Computing and Data Analysis for Environmental Applications /
Uncertainty in Engineering
Problem Set 5 (with solutions)
Due: Thursday, Oct. 23, 2003
Please turn in a hard copy of your MATLAB program as well as all printed outputs (tables,
plots, etc.) required to solve the problem.
Problem 1
Computing joint probabilities and correlations of a time series
Suppose that the total streamflows (in m
3
/month)
Q
t
and
Q
t+
1
over two successive
months
t
and
t+
1 are related by the following equation:
Q
t+
1
=
0.6
Q
t
+ e
t
t
= 1.
...10
In deterministic applications such time series expressions are solved one step at a time,
starting with a specified value of the initial value of the dependent (in this case, the
initial streamflow
Q
1
) and using a specified series of
e
t
values (for
t
= 10).
The resultis
a series of
Q
t
values for
t
> 1.
When
Q
1
and the
e
t
values are uncertain, we can use the time series equation to derive
the mean, variance, and covariance of the streamflow for
t
> 1.
These give a
probabilistic description of the temporally variable streamflow.
Suppose that the random excitation values
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 Spring '05
 GeorgeKocur
 Normal Distribution, Variance, Environmental Engineering, Probability theory, Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, Q2 Q2

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