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ps03_5

# ps03_5 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department...

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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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ps03_5 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department...

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