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

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Presentation transcript:

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: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 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:

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