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Binomial Distribution
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Parameters
Number of trials n
Probability of success p
Key Concepts
•
P(X=k) = C(n,k) · pᵏ · (1−p)ⁿ⁻ᵏ
for k = 0, 1, …, n
• Mean μ = np · variance σ² = np(1−p)
• Distribution is symmetric when p = 0.5, right-skewed for p < 0.5
• As n → ∞ and p fixed, the distribution approaches a Normal distribution (CLT)
• Required: fixed n, independent trials, constant p, binary outcomes
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