Proof #185: "Probability density function of a strictly increasing function of a continuous random variable" (pdf-sifct) #RandomProof statproofbook.github.io/P/pdf-sifct

Proof #439: "Construction of unbiased estimator for variance in multiple linear regression" (resvar-unbp) #RandomProof statproofbook.github.io/P/resvar-unbp

Proof #302: "Variance of the binomial distribution" (bin-var) #RandomProof statproofbook.github.io/P/bin-var

Proof #272: "Expectation of parameter estimates for simple linear regression" (slr-olsmean) #RandomProof statproofbook.github.io/P/slr-olsmean

Proof #21: "Relation of mutual information to joint and conditional entropy" (dmi-jce) #RandomProof statproofbook.github.io/P/dmi-jce

Proof #73: "Posterior model probability in terms of log Bayes factor" (pmp-lbf) #RandomProof statproofbook.github.io/P/pmp-lbf

Proof #517: "The variational free energy is a lower bound on the log model evidence" (fren-lme) #NewProof statproofbook.github.io/P/fren-lme

Proof #357: "Method of moments for beta-binomial data" (betabin-mome) #RandomProof statproofbook.github.io/P/betabin-mome

Proof #516: "Decompositions of the variational free energy" (fren-dec) #NewProof statproofbook.github.io/P/fren-dec

Proof #377: "F-statistic in terms of ordinary least squares estimates in one-way analysis of variance" (anova1-fols) #RandomProof statproofbook.github.io/P/anova1-fols

Proof #515: "Non-negativity of the Kullback-Leibler divergence" (kl-nonneg3) #NewProof statproofbook.github.io/P/kl-nonneg3

How to submit a new theorem to The Book of Statistical Proofs www.youtube.com/watch?v=ZMCH...

Proof #280: "Relationship between coefficient of determination and correlation coefficient in simple linear regression" (slr-rsq) #RandomProof statproofbook.github.io/P/slr-rsq

Proof #514: "Jensen's inequality" (jens-ineq) #NewProof statproofbook.github.io/P/jens-ineq

Proof #45: "Probability density function of the gamma distribution" (gam-pdf) #RandomProof statproofbook.github.io/P/gam-pdf

Proof #48: "Cumulative distribution function of the exponential distribution" (exp-cdf) #RandomProof statproofbook.github.io/P/exp-cdf

Proof #38: "Cumulative distribution function of the continuous uniform distribution" (cuni-cdf) #RandomProof statproofbook.github.io/P/cuni-cdf

Proof #391: "t-test for multiple linear regression using contrast-based inference" (mlr-t) #RandomProof statproofbook.github.io/P/mlr-t

Proof #141: "Cumulative distribution function of the discrete uniform distribution" (duni-cdf) #RandomProof statproofbook.github.io/P/duni-cdf

Proof #59: "Relation of continuous mutual information to marginal and joint differential entropy" (cmi-mjde) #RandomProof statproofbook.github.io/P/cmi-mjde

Proof #94: "Probability density function of the beta distribution" (beta-pdf) #RandomProof statproofbook.github.io/P/beta-pdf

Proof #14: "Relationship between R² and maximum log-likelihood" (rsq-mll) #RandomProof statproofbook.github.io/P/rsq-mll

Proof #165: "Log sum inequality" (logsum-ineq) #RandomProof statproofbook.github.io/P/logsum-ineq

Proof #150: "Convexity of the cross-entropy" (entcross-conv) #RandomProof statproofbook.github.io/P/entcross-c...

Proof #20: "Relation of mutual information to marginal and joint entropy" (dmi-mje) #RandomProof statproofbook.github.io/P/dmi-mje

Proof #264: "Probability density function of the F-distribution" (f-pdf) #RandomProof statproofbook.github.io/P/f-pdf

Proof #451: "Statistical test for intercept parameter in simple linear regression model" (slr-tint) #RandomProof statproofbook.github.io/P/slr-tint

Proof #225: "Conjugate prior distribution for Poisson-distributed data" (poiss-prior) #RandomProof statproofbook.github.io/P/poiss-prior

Proof #160: "Posterior distribution for multivariate Bayesian linear regression" (mblr-post) #RandomProof statproofbook.github.io/P/mblr-post

Proof #63: "Relationship between signal-to-noise ratio and R²" (snr-rsq) #RandomProof statproofbook.github.io/P/snr-rsq

Proof #457: "Mutual information of dependent and independent variables in the general linear model" (glm-mi) #RandomProof statproofbook.github.io/P/glm-mi

Proof #380: "F-statistics in terms of ordinary least squares estimates in two-way analysis of variance" (anova2-fols) #RandomProof statproofbook.github.io/P/anova2-fols

Proof #116: "Additivity of the Kullback-Leibler divergence for independent distributions" (kl-add) #RandomProof statproofbook.github.io/P/kl-add

Proof #329: "Multiple linear regression is a special case of the general linear model" (mlr-glm) #RandomProof statproofbook.github.io/P/mlr-glm

Proof #236: "Necessary and sufficient condition for independence of multivariate normal random variables" (mvn-ind) #RandomProof statproofbook.github.io/P/mvn-ind

Proof #213: "Log model evidence for the univariate Gaussian with known variance" (ugkv-lme) #RandomProof statproofbook.github.io/P/ugkv-lme

Proof #468: "Weak law of large numbers" (mean-wlln) #RandomProof statproofbook.github.io/P/mean-wlln

Proof #332: "t-distribution is a special case of multivariate t-distribution" (t-mvt) #RandomProof statproofbook.github.io/P/t-mvt

Proof #402: "Probability density function of the ex-Gaussian distribution" (exg-pdf) #RandomProof statproofbook.github.io/P/exg-pdf

Proof #82: "Mean of the continuous uniform distribution" (cuni-mean) #RandomProof statproofbook.github.io/P/cuni-mean

Proof #80: "Posterior distribution for multinomial observations" (mult-post) #RandomProof statproofbook.github.io/P/mult-post

Proof #513: "Expectation of a bilinear form" (mean-blf) #NewProof statproofbook.github.io/P/mean-blf

Thanks for sharing! 🤩

Proof #42: "Posterior distribution for the Poisson distribution with exposure values" (poissexp-post) #RandomProof statproofbook.github.io/P/poissexp-p...

Proof #328: "Gamma distribution is a special case of Wishart distribution" (gam-wish) #RandomProof statproofbook.github.io/P/gam-wish

Proof #148: "Convexity of the Kullback-Leibler divergence" (kl-conv) #RandomProof statproofbook.github.io/P/kl-conv

Proof #1: "Linear transformation theorem for the multivariate normal distribution" (mvn-ltt) #RandomProof statproofbook.github.io/P/mvn-ltt

Proof #204: "One-sample t-test for independent observations" (ug-ttest1) #RandomProof statproofbook.github.io/P/ug-ttest1

Proof #512: "Partition of a cross-covariance matrix into expected values" (covmatcross-mean) #NewProof statproofbook.github.io/P/covmatcros...

Proof #216: "Expectation of the log Bayes factor for the univariate Gaussian with known variance" (ugkv-lbfmean) #RandomProof statproofbook.github.io/P/ugkv-lbfmean