CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Statistical inference (Sec. )

Introduction and motivation  Practical application of probability models:  Observations:  Population:  Sample:

Introduction and motivation  What is inference?  Representativeness of the sample:

Types of inference problems  Parameter estimation:  Determination of the distribution:  Hypothesis testing:

Parameter estimation  Maximum likelihood:

Parameter estimation: Bernoulli trials  Parameters to be estimated:  Observations:  Likelihood function:

Parameter estimation: Bernoulli trials  Maximum likelihood estimate:  Example:

Parameter estimation: Binomial distribution  Parameter to be estimated:  Observations:

Parameter estimation: Binomial distribution (contd..)  Likelihood function:

Parameter estimation: Binomial distribution (contd..)  Maximum likelihood estimate:

Parameter estimation: Binomial distribution (contd..)  Example:

Parameter estimation: Geometric distribution  Parameters to be estimated:  Observations:

Parameter estimation: Geometric distribution (contd..)  Likelihood function:

Parameter estimation: Geometric distribution (contd..)  Maximum likelihood estimate:

Parameter estimation: Geometric distribution (contd..)  Example: