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EE381-Project 6 Conclusion Markov chains and Probability Solved

Simulating general two-state discrete time Markov chain and evaluating its steady state.

Exercise.

For the general two-state process the transition matrix  .  Determine the steady state vector for the state vector [𝜑0 𝜑1].

 

Computer Solution.

A computer simulation of two states (project 3) will be modified to determine the steady state.

 

Probability

The Birthday Problem

This a problem that can be solved using a computational solution.

Assume 365 days in a year and that people’s birthdays are randomly distributed throughout the year.  With 𝑘 people in a room, what is the probability that at least two have the same birthday?

Theory:

 

Computer Solution:

 

Poisson Random Variable

Write a program in Python that recursively generates Poisson probabilities.  Note the change in shape as the parameter increases.

 

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