1. CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Continuous random variables Uniform and Normal distribution (Sec. 3.1, 3.4.6-3.4.7)

2. Continuous random variables  Discrete vs. Continuous random variables:

3. Continuous random variables (contd..)  Event definition:  Cumulative Distribution Function (CDF):

4. Continuous random variables (contd..)  CDF of discrete vs. continuous random variables:

5. Continuous random variable (contd..)  Relationship between density and distribution functions:

6. Continuous random variable (contd..)  Properties of distribution function:

7. Continuous random variables (contd..)  Density function of continuous vs. discrete random variables:

8. Uniform distribution (contd..)  Density:  Distribution function:

9. Uniform distribution (contd..)  Parameters of the uniform distribution:  Verification of the CDF of uniform distribution:

10. Normal distribution  Density function:  Shape of the density function:

11. Normal distribution (contd..)  Parameters of the normal distribution:  Distribution function:  Standard normal distribution:

12. Normal distribution (contd..)  Conversion of a non-standard random variable to a standard normal variable:

13. Normal distribution (contd..)  Example:

14. Normal distribution (contd..)  Central limit theorem: