1. Tutorial 12 Cover: *Conditional Distribution and Expectation *Assignment 7 8 Conica, Cui Yuanyuan

2. Erlang  r-stage Erlang Cold Standby

3. Hypoexponential  r-stage Hypo Warm Standby

4. Laplace Transform Continuous non-negative r.v.

6. Z Transform Discrete non-negative r.v.

7. Z Transform

8. Conditional Distribution

9. Discrete X and Y

10. Example

11. Continuous X and Y

12. Example

13. Discrete X and Continuous Y

14. Example  Consider a file server whose work load may be divided into r distinct classes. For class i, the CPU service time is exponential distributed with i. Y : the service time of a job X : the job class

15. Continuous X and Discrete Y

16. Example X : the service time of a request to a web server X~EXP(  ) Y : the number of requests arriving Y~Poisson( t)

17. Conditional Expectation

20. Example: r-stage Hyperexponential

21. Example

24. Imperfect fault coverage and R(t) X=lifetime of a system Y=fault class

25. Example

27. Random Sum

29. Example

34. Thanks for coming! Questions?