lec . 08 – discrete (and continuous) probability distributions

Lec. 08 – Discrete (and Continuous) Probability Distributions

Independence

Discrete Uniform Distribution

What are some examples of this?

Binomial Distribution

If interested in obtaining the probability of r successes out of n trials over a range of r, when the probability is known – see our first example of the course!

Poisson Distribution

A Poisson experiment is a statistical experiment that has the following properties:The experiment results in outcomes that can be classified as successes or failures.The average number of successes (μ) that occurs in a specified region is known.Probability that a success will occur is proportional to the size of the region.Probability that a success will occur in an extremely small region is virtually zero.

Poisson Distribution Example

1. First, code up the Poisson distribution for a mean of your choosing, and display the histogram.

2. Write a MATLAB code to answer the following questions about floods:

Negative Binomial DistributionBinomial = Distribution of the number of successes in a fixed number of trials

Negative Binomial = Distribution of the minimum number of trials required to produce a fixed number of successes (e.g. number of wells drilled to find 3 exploitable reservoirs)

1. Geometric distribution – simplest form – defines prob. distrib. of trials needed to obtain the 1st success:

Pr(X=x)=(1-p)x-1p

2. Prob. of number of trials required to obtain exactly r successes:

Continuous Random Variables = p.d.f.’s

Poisson Distribution (discrete) Exponential Distribution (continuous)