4.10 Introduction to the Binomial Distribution

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The Binomial Setting (BINS)

The binomial distribution

BINS — Four conditions for a binomial setting:

Binary: each trial has exactly two outcomes (success or failure)
Independent: trials are independent of each other
Number fixed: the number of trials ${n}$ is fixed in advance
Same probability: each trial has the same probability of success ${p}$

If BINS conditions are met: ${X \sim B(n, p)}$

Example: Flip a fair coin 10 times; count number of heads.

Binary: head or tail ✓
Independent: flips don't affect each other ✓
n = 10 fixed ✓
p = 0.5 for each flip ✓ → ${X \sim B(10, 0.5)}$

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