Statistics · Statistical distributions
Chapter 1 · 3
The idea
The binomial distribution as a model
When the count of "successes" in a fixed number of repeated trials follows a binomial distribution X ~ B(n, p): the four conditions (a fixed number of trials, two outcomes per trial, a constant probability of success, and independent trials), how to identify n and p from a context, how to state a condition for a binomial model, and when the binomial is NOT appropriate.
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Statistics · Statistical distributions
The binomial distribution as a model
When the count of "successes" in a fixed number of repeated trials follows a binomial distribution X ~ B(n, p): the four conditions (a fixed number of trials, two outcomes per trial, a constant probability of success, and independent trials), how to identify n and p from a context, how to state a condition for a binomial model, and when the binomial is NOT appropriate.
Why it works
Counting successes in repeated trials
Many situations are the same experiment repeated over and over, where each repeat either "succeeds" or "fails". If you count the number of successes, that count often follows a binomial distribution, writtenwhere is the number of trials and is the probability of success on each trial. (So in , there are trials each with success probability .)
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