stat310
Probability summary
Vocabulary
You should know the definitions of the following words/phrases. (You wont’ need to regurgitate these definitions in an exam, but you’ll need them to understand the questions and solve the problems). Where possible, you should be able to express the phrase in both words and mathematics.
- Random experiment
- Sample space
- Event
- Mutually exclusive
- Exhaustive
- Partition
- Probability function, including the three defining criteria, and the other important properties
- Equally likely events
- Combination
- Permutation
- Conditional probability, including the properties that it satisfies
- Independence
- Prior and posterior probability
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Basic set algebra.
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Given a word problem, define appropriate sample space and events, and convert problem to a mathematical question.
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Multiplication principle
- Sampling with and without replacement
- Correctly reduce the number of outcomes if order doesn’t matter
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The basic tools of rearranging probability problems (including when it is appropriate to use each tool):
- Taking complements.
- Multiplication rule / replacing intersections with conditioning
- Convert unions to sums
- Convert intersection to products (if independent)
- Law of total probability.
- Bayes rule = multiplication rule + law of total probability
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Convert conditional probabilities to natural frequencies.