# Probability Distributions

## Can you name the common probability distributions?

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DescriptionDistribution
1. By the central limit theorem, large sums of random variables converge in distribution to this
2. #1, with mean=0 and variance=1
3. For a population of independent #1s, standardizing the sample mean using the sample variance gives this
4. The sum of the squares of independent #2s; used in tests of independence
5. The ratio of two #4s; used in likelihood ratio tests, ANOVA
6. The outcome of a single trial with sample space {0,1}
7. The number of successes in a series of independent repeated trials
8. The number of successes in a series of draws without replacement
9. The number of independent trials up to and including the first success
DescriptionDistribution
10. The number of independent trials up to and including the rth success
11. The total number of occurrences in a given time period, if the event occurs independently of previous occurences and at a fixed average rate
12. The (continuous) time before the first occurrence of an event that occurs as in #11
13. The (continuous) time until the rth occurrence of an event that occurs as in #11
14. A family of distributions with parameters alpha and lambda; #4, #12, and #13 are special cases
15. Defined on [0,1] with shape parameters alpha and beta
16. f(x) is constant over a finite set
17. Commonly used in reliability engineering to model failure probabilities
18. Used to model the frequency of words in a language
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Last Updated: Feb 16, 2017

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