Fall 2003 Final: EE/CpE/PEP 345 - Modeling and Simulation

Problem 1:

This is how the data was generated

But this is the data that was really used

Plot histogram with optimal number of bins:

Problem 2:

This is how data was generated:

But this is the data that was used:

For 5% level of significance, find z.a, such that f(-z.a)=.025 and f(z.a)=.975

Since Z.0 < 1.96, this number of runs looks reasonable.

Problem 4

For a poisson process,

Probability that n is odd:

Problem 5:

Problem 6:

Generate a R.V.

This is how I originally generated the values. I have to use fixed values
for the solution, since the worksheet gets recalculated each time it is accessed.

Create a second R.V. having dependency with first R.V.

These were the values used in the exa,:

Compute the correlation. I am using the Mathcad built in function, but this
is the same as using the expected value function.

If you want to see that the corr function generates the correlation we defined in class:

You can also observe correlation in the scatter plot to see correlation

Problem 7:

Problem 10:

Problem 11:

Generate a series of pseudo random numbers using a linear congruential random number generator

R(X) is the autocorrelation of X.
Notice I am calculating correlation with
different offsets in the sequence.

Search over middle range for largest:

Largest value:

Compare to the built in random number generator:

Problem 12:

Here are the correct expressions for mean and variance

Generate a triangularly distributed R.V

And test the expressions: