Exam 1 Study Guide
The variance of the negative binomial distribution in terms of and
It turns out that a Poisson random variable can be viewed as a special limiting
case of a negative binomial random variable in which the parameter is
allowed to become

Quiz 2 Review Guide
Interpreting the information
The formal definition of the curvature of a curve is the following.
Here is the angle the tangent line makes with the curve and s is arc length.
Thus curvature is the rate at which you turn (in radians per

Lecture 9
Normal models with a transformed response
Model 6: Arrhenius model
The Arrhenius model is just an ordinary regression model in which both the
response and predictor are log-transformed. The square root transformation is
viewed as a less severe t

Lecture 8 Notes
Gamma Function
The gamma function is defined as follows.
Although the integrand contains two variables, x and , x is the variable of
integration and will disappear once the integral is evaluated. So the gamma
function is solely a function

Lecture 7 Notes
Negative Binomial Distribution
I finish our survey of probability distributions useful in ecology with a
discussion of the negative binomial distribution.
Basic characteristics
A negative binomial (NB) random variable is discrete. A typic

Lecture 6 Notes
Obtaining the variances of treatment means from ANOVA models
In lecture 5 we created mean profile plots to display estimated treatment means and their
95% confidence intervals from ANOVA models. To obtain the estimates we used
the effect f

HW 1
1. The probability of obtaining a random sample
denote a random sample of size n.
2.
3.
The score (gradient) vector
4.
The maximum likelihood estimates (MLEs) of and are those values that make
the log-likelihood (and hence the likelihood) as large as

Final Comprehensive Exam Study Guide
Review of likelihood theory
The probability of obtaining a random sample
Let
denote a random sample of size n. We wish to compute
the probability of obtaining this particular sample for different probability
models in

Exam 2 Study Guide
Methods of Estimation
A probability model is used to describe the behavior of a response variable. As
I explained in lecture 4, a useful way to think of a probability model in a
regression setting is as a data-generating mechanism. The

Quiz 4
Some of the not so nice properties of MLEs
1. Maximum likelihood estimators are often biased.
2. Maximum likelihood estimators need not be unique.
3. Maximum likelihood estimators may not exist.
4. Maximum likelihood estimators can be difficult to