Proof #532: "Cross-validated log Bayes factor for multinomial observations" (mult-cvlbf) #NewProof
statproofbook.github.io/P/mult-cvlbf

Proof #531: "Cross-validated log Bayes factor for binomial observations" (bin-cvlbf) #NewProof
statproofbook.github.io/P/bin-cvlbf

Proof #530: "Partial correlation of random variables which are jointly multivariate normal distributed" (mvn-corrpart) #NewProof
statproofbook.github.io/P/mvn-corrpart

Proof #529: "Conditional correlation of random variables which are jointly multivariate normal distributed" (mvn-corrcond) #NewProof
statproofbook.github.io/P/mvn-corrcond

Proof #528: "The third standardized moment equals the skewness" (momstand-3rd) #NewProof
statproofbook.github.io/P/momstand-3rd

Proof #527: "The second standardized moment equals one" (momstand-2nd) #NewProof
statproofbook.github.io/P/momstand-2nd

Proof #526: "The first standardized moment equals zero" (momstand-1st) #NewProof
statproofbook.github.io/P/momstand-1st

🫠

Proof #525: "Marginal distributions of the multivariate t-distribution" (mvt-marg) #NewProof
statproofbook.github.io/P/mvt-marg

Proof #524: "Second-order expectations for the matrix-normal distribution" (matn-meanso) #NewProof
statproofbook.github.io/P/matn-meanso

Thanks! 👍

Proof #523: "Expectation of quadratic forms for the matrix-normal distribution" (matn-meanqf) #NewProof
statproofbook.github.io/P/matn-meanqf

DOI or URL?

Proof #522: "Cross-covariance matrices of the matrix-normal distribution" (matn-ccm) #NewProof
statproofbook.github.io/P/matn-ccm

Consider this a compliment... 😁

Haha... 😂 Nice to hear it's rigorous! Any ideas to make it less messy? 🤔

Proof #521: "Chi-squared distribution is a special case of gamma distribution" (chi2-gam2) #NewProof
statproofbook.github.io/P/chi2-gam2

Proof #428: "Maximum-a-posteriori estimation for multinomial observations" (mult-map) #RandomProof
statproofbook.github.io/P/mult-map

Proof #24: "Mean of the categorical distribution" (cat-mean) #RandomProof
statproofbook.github.io/P/cat-mean

Proof #309: "Corrected Akaike information criterion for multiple linear regression" (mlr-aicc) #RandomProof
statproofbook.github.io/P/mlr-aicc

Proof #113: "Relation of discrete Kullback-Leibler divergence to Shannon entropy" (kl-ent) #RandomProof
statproofbook.github.io/P/kl-ent

Proof #112: "Relationship between gamma distribution and standard gamma distribution" (gam-sgam) #RandomProof
statproofbook.github.io/P/gam-sgam

Proof #135: "Projection matrix and residual-forming matrix are idempotent" (mlr-idem) #RandomProof
statproofbook.github.io/P/mlr-idem

Proof #261: "Addition of the differential entropy upon multiplication with invertible matrix" (dent-addvec) #RandomProof
statproofbook.github.io/P/dent-addvec

Proof #51: "Mode of the exponential distribution" (exp-mode) #RandomProof
statproofbook.github.io/P/exp-mode

Proof #257: "Probability mass function of a sum of independent discrete random variables" (pmf-sumind) #RandomProof
statproofbook.github.io/P/pmf-sumind

Proof #371: "Ordinary least squares for two-way analysis of variance" (anova2-ols) #RandomProof
statproofbook.github.io/P/anova2-ols

Proof #308: "Bayesian information criterion for multiple linear regression" (mlr-bic) #RandomProof
statproofbook.github.io/P/mlr-bic

Proof #25: "Mean of the multinomial distribution" (mult-mean) #RandomProof
statproofbook.github.io/P/mult-mean

Proof #414: "Equivalence of operations for model evidence and log model evidence" (lme-mean) #RandomProof
statproofbook.github.io/P/lme-mean