Linked from

The 24 pages that link to Independence (probability theory), each with the reason it gives.

• Probability theoryRelated: Independence determines when joint probabilities factor into simpler terms.

• ProbabilityRelated: Independence determines when joint probabilities can be calculated by multiplication.

• Probability spaceRelated: The probability measure makes independence a relation between events.

• Borel–Cantelli lemmaRelated: The second lemma needs independence, unlike the first.

• Bernoulli trialRelated: Repeated Bernoulli trials often assume independence, though a single trial needs no such assumption.

• Probability-generating functionRelated: Independence explains why generating functions multiply when random variables are added.

• Chernoff boundRelated: For independent summands, their moment-generating functions multiply, simplifying the bound.

• Hidden Markov modelRelated: Observations are conditionally independent given their corresponding states in the standard model.

• Jacob BernoulliRelated: The repeated-trial assumptions make independent outcomes central to the theorem.

• Negative binomial distributionRelated: The trial-sequence formula assumes each outcome leaves later trial probabilities unchanged.

• Chi-squared distributionRelated: Independence is required among the normal variables in the defining sum.

• Poisson limit theoremRelated: Independent trials are the standard binomial setting behind the theorem.

• Condorcet's jury theoremRelated: Independent votes let individual accuracy translate cleanly into a group-level probability.

• Bienaymé's identityRelated: Independence is the condition that eliminates cross terms in Bienaymé's identity.

• Cochran's theoremRelated: Cochran’s theorem turns algebraic orthogonality conditions into independence of quadratic forms.

• Cramér's decomposition theoremRelated: Independence makes the characteristic function of the sum a product.

• Law of Truly Large NumbersRelated: For independent trials, the probability of no occurrences multiplies across opportunities.