AP Statistics Curriculum 2007 Distrib Multinomial
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General Advance-Placement (AP) Statistics Curriculum - Multinomial Random Variables and Experiments
The multinomial experiments (and multinomial distribtuions) directly extend the their bi-nomial counterparts.
- Examples of Multinomial experiments
- Rolling a hexagonal Die 5 times: Where the outcome space is the colection of 5-tuples, where each element is a value such that: .
- The Multinomial random variable (RV): Mathematically, a (k) multinomial trial is modeled by a random variable
If p_{i} = P(X = x_{i}), then:
- expected value of X, .
- standard deviation of X, .
Synergies between Binomial and Multinomial processes/probabilities/coefficients
- The Binomial vs. Multinomial Coefficients
- The Binomial vs. Multinomial Formulas
- The Binomial vs. Multinomial Probabilities
Example
Suppose we study N independent trials with results falling in one of k possible categories labeled 1,2,cdots,k. Let p_{i} be the probability of a trial resulting in the i^{th} category, where . Let N_{i} be the number of trials resulting in the i^{th} category, where .
For instance, suppose we have 9 people arriving at a meeting according to the following information:
- P(by Air) = 0.4, P(by Bus) = 0.2, P(by Automobile) = 0.3, P(by Train) = 0.1
- Compute the following probabilities
- P(3 by Air, 3 by Bus, 1 by Auto, 2 by Train) = ?
- P(2 by air) = ?
SOCR Multinomial Examples
References
- SOCR Home page: http://www.socr.ucla.edu
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