lec. 08 – discrete (and continuous) probability distributions
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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)