1. CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Confidence intervals

2. Motivation  Point estimate:  Interval estimate:

3. Motivation (contd..)  Example:

4. Motivation (contd..)  Frequentist’s interpretation:

5. Estimation of confidence interval  Distribution of the mean of normal random variables:

6. Estimation of confidence interval (contd..)  Conversion to standard normal random variable:

7. Estimation of confidence interval (contd..)  Obtaining an interval estimate for standard normal random variable:

8. Estimation of confidence interval (contd..)  Obtaining an interval estimate for standard normal random variable:

9. Estimation of confidence interval (contd..)  Obtaining an interval estimate for standard normal random variable:

10. Estimation of confidence interval (contd..)  Converting to an interval estimate for the mean of normal random variables:

11. Estimation of confidence interval (contd..)  Example: