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Binomial Distribution
High School
Definition
The binomial distribution models the number of successes in n independent trials, each with success probability p.
Formulas
P(X = k) = \binomnk p^k (1-p)^n-k
Binomial PMF
E[X] = np
Expected value of binomial
Var(X) = np(1-p)
Variance of binomial
Examples
Example 1
Find P(exactly 6 heads) when flipping a coin 10 times.
Applications
Quality Control
Defect rate analysis
Medicine
Drug efficacy analysis
Elections
Poll analysis
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