CSE 221: Probabilistic Analysis of Computer Systems

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CSE 221 Probabilistic Analysis of Computer
Systems
Topics covered Statistical inference (Sec. )
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Introduction and motivation

• Practical application of probability models
• Observations
• Population
• Sample

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Introduction and motivation

• What is inference?
• Representativeness of the sample

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Types of inference problems

• Parameter estimation
• Determination of the distribution
• Hypothesis testing

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Parameter estimation

• Maximum likelihood

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Parameter estimation Bernoulli trials

• Parameters to be estimated
• Observations
• Likelihood function

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Parameter estimation Bernoulli trials

• Maximum likelihood estimate
• Example

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Parameter estimation Binomial distribution

• Parameter to be estimated
• Observations

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Parameter estimation Binomial distribution
(contd..)

• Likelihood function

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Parameter estimation Binomial distribution
(contd..)

• Maximum likelihood estimate

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Parameter estimation Binomial distribution
(contd..)

• Example

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Parameter estimation Geometric distribution

• Parameters to be estimated
• Observations

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Parameter estimation Geometric distribution
(contd..)

• Likelihood function

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Parameter estimation Geometric distribution
(contd..)

• Maximum likelihood estimate

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Parameter estimation Geometric distribution
(contd..)

• Example