Probability & Statistics
Reference

Distributions, tests, and formulas. From basics to advanced statistical methods.

Probability

Basic Rules

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
P(A|B) = P(A ∩ B) / P(B)
P(A') = 1 - P(A)

Conditional Probability

P(A|B) = P(B|A) · P(A) / P(B)

Distributions

Normal Distribution

f(x) = (1/σ√(2π)) × 
       e^(-(x-μ)²/(2σ²))

Binomial Distribution

P(X = k) = C(n,k) × 
          p^k × (1-p)^(n-k)

Poisson Distribution

P(X = k) = (λ^k × e^(-λ)) / k!

Statistical Tests

t-test

t = (x̄ - μ) / (s / √n)
df = n - 1

Chi-square Test

χ² = Σ((O - E)² / E)
df = (r-1)(c-1)

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