Data, Statistics & Probability

Advanced statistics, distributions and combinatorics

Explanation

Statistical Inference

  • Normal distribution: bell-shaped; 68% of data within 1 SD; 95% within 2 SD; 99.7% within 3 SD.
  • Correlation vs causation: a strong correlation does not imply one thing causes the other.
  • Bias in sampling: convenience sampling, self-selection bias can skew results.

Combinatorics

  • Permutation (order matters): P(n,r) = n!/(n−r)!
  • Combination (order doesn't matter): C(n,r) = n!/[r!(n−r)!]
  • Binomial theorem: (a+b)ⁿ — the coefficients come from Pascal's triangle (= C(n,r)).

Probability

  • Bayes' theorem: P(A|B) = P(B|A)·P(A) / P(B)
  • Geometric probability: probability = (favourable area)/(total area)
  • Expected value: E(X) = Σ[xᵢ · P(xᵢ)]
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