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### Exam Information

The Final Exam covers the entire course, however the emphasis is on the material not covered in Quiz 1 and Quiz 2. |

### Preparation Activities

Review the Practice Exams and Solutions from previous years:

- Spring 2009 Final Exam (PDF); Spring 2009 Final Exam Solutions (PDF)
- Fall 2009 Final Exam (PDF); Fall 2009 Solutions Final Exam (PDF)

### Exam and Solutions

Take the exam on your own and check your answers when you’re done.

### Conclusion

Congratulations! You’ve completed *Probabilistic Systems Analysis and Applied Probability*. You have learned all the basic tools of probability theory, the main concepts of statistical inference (both Bayesian and classical), and has been exposed to some classes of random processes. This is already enough to allow application of probabilistic methods to many real-world applications.

### Further Study

For those wishing further study, there are the following possible directions:

- A deeper study of the mathematical foundations of the subject, relying on measure theory [
*6.436J Fundamentals of Probability*,*18.175 Theory of Probability*,*18.176 Stochastic Calculus*] - Further classes on discrete random processes [
*6.262 Discrete Stochastic Processes*,*18.445 Introduction to Stochastic Processes*] or random processes that evolve in continuous time over continuous state spaces [*15.070 Advanced Stochastic Processes*] - Classes on statistics and inference [
*15.097 Prediction: Machine Learning and Statistics*,*18.443 Statistics for Applications*] and associated algorithms [_6.438 Algorithms for Inference_]

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