1. CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Expectation of random variables Moments (Sec. 4.1-4.2)

2. Introduction  Example:  Expectation/average:  Median  Mode

3. Expectation  Definition:

4. Expectation (contd..)  Example: Average number of heads in a sequence of three coin tosses

5. Expectation (contd..)  Exponential random variable:

6. Expectation (contd..)  Mean of a exponential random variable:

7. Expectation (contd..)  Expectation of a uniform random variable:

8. Expectation (contd..)  Expectation of a function of a random variable:

9. Expectation (contd..)  Example: Cost function with a sequence of three coin tosses.

10. Expectation (contd..)  Expectation of a power function:

11. Variance  Measure the spread of a distribution:

12. Variance (contd..)  Definition of variance:

13. Variance (contd..)  Implications of variance: