Introduction, read p. 56-65 Appendix

and section 1.4.4 p. 72-73

-Conditional Probability: why is it useful?

-Introduction to discrete random variables,

–Read pages 66-75 of the notes for next class

-Elementary properties of

discrete random variables, Expected values and variances

-examples

• HW1, due Sept 15
• R-Intro needed for HW1

For Thursday 3rd: no reading necessary, we will continue with Expected values

-More on expected values

-Conditional probability distributions

-Conditional expectation

-Mark-recapture, sampling with replacement

-R program for the hierarchical binomial survival model.

-Mark-recapture, sampling with replacement

-The binomial distribution

-The likelihood function

-Mark-recapture, sampling without replacement

-The hypergeometric distribution

– Comparison with sampling with replacement using means, variances and covariances

-Why adopting different probability models for the same experimental setting is important?

-Relationship between the binomial model and the hypergeometric model using conditional probability!!

-Introduction to the Poisson Process as a limit to the Binomial model

– -Introduction to the Poisson Process as a limit to the Binomial model

Waiting times: introducing the exponential distribution using a Poisson process.

How do you write the likelihood function for a continuous probability model?  The MLE of the exponential rate parameter

Waiting times until the kith event:  introducing the Gamma distribution using a Poisson process

-The Gamma function

– Connections between the Gamma model and the Poisson process

-Heterogeneity in Ecology, pages 28-32 of the class notes:

-the negative binomial distribution

-the zero inflated poisson distribution

Note pages 32-41:

Probability Generating Functions and

-the geometric distribution

-the negative binomial distribution

-the log-series distribution

-Return HW to students!!!

Note pages 32-41:

Probability Generating Functions and

-the geometric distribution

-the negative binomial distribution

-the log-series distribution

-The Multinomial distribution, part I

-The Multinomial distribution, part II

-Likelihood Ratio test

-Multinomial Goodness of fit test

-Fitting the Poisson process data to counts, comparing to Negative Binomial, Zero Inflated Poisson, and other models.