HW 1
1. A two-stage cluster sample is an extension of a one-stage cluster sample
in that it adds a second sampling stage. After selecting the clusters
(primary sample units) we then choose a subsample of units from each
cluster (secondary sample units), g

Study Aid 2
Negative binomial distribution
A negative binomial (NB) random variable is discrete.
A typical use would be as a model for count data.
The negative binomial distribution is bounded on one side. It is bounded
below by 0, but is theoretically un

Study Aid 1
A Poisson random variable is discrete.
A typical use would be as a model for count data.
The Poisson distribution is bounded on one side. It is bounded below by
0, but is theoretically unbounded above.
Example: Number of cases of Lyme disease

Lecture Notes 4
Derivation of the formula for the binomial probability mass function
Suppose we have five independent Bernoulli trials with the same
probability p of success on each trial.
If we observe the event:
, i.e., three successes
and two failures

Lecture Notes 3
Binomial distribution
A binomial random variable is discrete.
It records the number of successes out of n trials
The idealized exemplar of the binomial distribution is an experiment in
which we record the number of heads obtained when a co

Lecture Notes 2
A probability density function satisfies three properties.
1. It's a non-negative function
. If we're dealing with a
probability mass function instead then we also
have
.
2. If we sum the probability function over all possible value of x w

Lecture Notes 1
The Role of Probability Models in Model-based Inference
Model-based inference versus design-based inference.
o
In model-based inference we try to account for the design
imperfections in our "experiment" by building a model.
o
We cant corre

In Class Assignment 2
In sampling theory a distinction is made between the population and the
sample.
o
The population is the entity P to which you want your conclusions to
apply.
o
The sample is a subset S of P. It is the set of units for which you
have

In Class Assignment 1
In environmental studies the assumption of equal selection probabilities
is almost never realized. Observations typically come in groups.
o In surveys of popular opinion, the survey instrument may be sent
to households and then all a

Study Aid 3
Overdispersion
In describing the Poisson and negative binomial distributions we noted
that the variance and the mean are related. We stated the following.
Poisson:
Negative binomial:
where is called the dispersion parameter (also the size or