1. Lecture 1 Experiments, Models and Probabilities

2. Outline

3. Definition An outcome of an experiment is any possible observation of that experiment. The sample space of an experiment is a set of all possible outcomes. An event is a set of outcomes of an experiment. An event space is a set of events.

4. Telephone Usage Question: Determine the probability of a long call.

5. Conditional Probability

6. Resistor Variability (1)

7. Resistor Variability(2)

8. Traffic Lights

10. Permutations Shuffle the deck and choose three cards in order. How many outcomes are there? – 52 x 51 x 50

12. Choose k objects out of n

13. Resistor Variability(2)

14. Transmission of Information

15. Transmission of Data Packets

17. Definitions For n trials of a subexperiment with sample space S={s 0,,,,s m-1 }, we want to find the number observations sequences in which s 0 appears n 0 times, s 1 appears n 1 times, and so on.

18. Chip Fabrication How many elements are in the entire set of possible sequences? n 0 =2 n 1 =2 n 2 =3 n 3 =3

20. Multinomial Coefficient

21. Example

22. Chip Fabrication (3)

23. Reliability

24. Redundant Parts

25. Matlab

26. factorial(n)

27. nchoosek(n,k)

28. Flip a Fair Coin 4 Times

30. ceil()

31. Execution

32. Plot the histogram

33. Packets

34. Matlab Code

35. # of packets in simulation n=100 n=10000n=100000