1. Lec. 08 – Discrete (and Continuous) Probability Distributions

2. Independence

3. Discrete Uniform Distribution What are some examples of this?

4. 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!

5. Poisson Distribution A Poisson experiment is a statistical experiment that has the following properties: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.

6. 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:

7. Negative Binomial Distribution Binomial = 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 1 st success: Pr(X=x)=(1-p) x-1 p 1.Prob. of number of trials required to obtain exactly r successes:

8. Continuous Random Variables = p.d.f.’s Poisson Distribution (discrete)  Exponential Distribution (continuous)