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Probability & Sampling

  • Discusses Markov chains, transition probabilities, and the transition probability matrix.
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  • The page will calculate the following: Exact binomial probabilities, Approximation via the normal distribution, Approximation via the Poisson Distribution. This page will calculate and/or estimate binomial probabilities for situations of the general "k out of n" type, where k is the number of times a binomial outcome is observed or stipulated to occur, p is the probability that the outcome will occur on any particular occasion, q is the complementary probability (1-p) that the outcome will not occur on any particular occasion, and n is the number of occasions.

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  • This website lists five different types of probability sampling, giving the advantages and disadvantages of each.
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  • This article gives a description of typical sources of error in public opinion polls. It gives a short but insightful explanation of what the margin of error indicates as well as other common errors in opinion polls.
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  • An application of Bayes Theorem that performs the same calculations for the situation where the several probabilities are constructed as indices of subjective confidence.

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  • This page will generate a graphic and numerical display of the properties of a binomial sampling distribution, for any values of p and q, and for values of n between 1 and 40, inclusive.

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  • Students can sample numerous bags of M&Ms. A plot of the relative frequency of each color is continually updated above the sampling frame. Each sample bag of M&Ms contains 56 candies.
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  • This exercise will help the user understand the logic and procedures of hypothesis testing. To make best use of this exercise, the user should know how to use a z table to find probabilities on a normal distribution, and how to calculate the standard error of a mean. Relevant review materials are available from the links provided. The user will need a copy of the hypothesis testing exercise (link is provided), a table for the standardized normal distribution (z), and a calculator. The user will be asked several questions and will be given feedback regarding their answers. Detailed solutions are provided, but users should try to answer the questions on their own before consulting the detailed solutions. The end of the tutorial contains some "thought" questions.
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  • This site describes in detail 5 different types of random sampling, giving examples, definitions, and procedures.
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