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Understanding Discrete and Continuous Probability Distributions

Explore examples and applications of discrete uniform distribution, binomial distribution, Poisson experiment, Poisson distribution, negative binomial distribution, geometric distribution, and continuous random variables in MATLAB coding. Learn about the probabilities of success and failures in various statistical experiments.

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Understanding Discrete and Continuous Probability Distributions

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  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. 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

  6. First, code up the Poisson distribution for a mean of your choosing, and display the histogram. Write a MATLAB code to answer the following questions about floods: Poisson Distribution Example

  7. 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) Geometric distribution – simplest form – defines prob. distrib. of trials needed to obtain the 1st success: Pr(X=x)=(1-p)x-1p Prob. of number of trials required to obtain exactly r successes: Negative Binomial Distribution

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

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