What is sampling

Figure 1

lake with frogs and two samples drawn from them
Sampling frogs in a lake

What is a probability distribution?

Figure 1

possible outcomes of sampling ten frogs
Binomial sampling

Figure 2

graph showing probability distribution of frog catches
Sampling probabilities

Figure 3

example graphs for discrete and continuous probability distributions
Types of probability distributions

The binomial distribution

Figure 1

possible outcomes of sampling 10 frogs

Figure 2

example graph for binomial probability distribution
The binomial distribution

Probability distributions in R

Figure 1

The Poisson distribution

Figure 1

frog cartoon demonstrating how the Poisson is derived from the Binomial distribution
The Poisson distribution is a special case of the binomial

Figure 2

lake with only one sort of frogs
Poisson example

Figure 3

Simulations in R

The Gamma-Poisson distribution

Figure 1

Figure 2

plots demonstrating a mixture distribution from gamma and poisson
The Gamma Poisson distribution

The Gaussian distribution

Figure 1

plot of Gaussian distribution
Gaussian probability density function

Visualizing distributions

Figure 1

histogram plot

Figure 2

histogram and ecdf plot

Figure 3

histogram, ecdf, and qq plot

Histograms in R

Figure 1

Figure 2

Figure 3

The cumulative distribution function

Figure 1

Figure 2

The QQ-plot

Figure 1

Figure 2

Figure 3

Figure 4

Summary

Exercises