Merge pull request #72 from StatProofBook/master

update to master

Author: JoramSoch

D/rexp.md

@@ -10,7 +10,7 @@ date: 2020-11-19 04:10:00
 title: "Random experiment"
 chapter: "General Theorems"
 section: "Probability theory"
-topic: "Random variables"
+topic: "Random experiments"
 definition: "Random experiment"
 
 sources:
@@ -29,10 +29,10 @@ username: "JoramSoch"
 
 **Definition:** A random experiment is any repeatable procedure that [results in one](/D/rvar) out of a well-defined set of possible outcomes.
 
-* The set of possible outcomes is called sample space.
+* The set of possible outcomes is called [sample space](/D/samp-spc).
 
 * A set of zero or more outcomes is called a [random event](/D/reve).
 
 * A function that maps from events to probabilities is called a [probability function](/D/dist).
 
-Together, sample space, event space and probability function characterize a random experiment.
+Together, [sample space](/D/samp-spc), [event space](/D/eve-spc) and [probability function](/D/prob-spc) characterize a random experiment.

D/rvar.md

@@ -31,6 +31,6 @@ username: "JoramSoch"
 
 * informally, as a real number $X \in \mathbb{R}$ whose value is the outcome of a [random experiment](/D/rexp);
 
-* formally, as a [measurable function](/D/meas-fct) $X$ defined on a [probability space](/D/prob-spc) $(\Omega, \mathcal{F}, P)$ that maps from a sample space $\Omega$ to the real numbers $\mathbb{R}$ using an event space $\mathcal{F}$ and a [probability function](/D/dist) $P$;
+* formally, as a [measurable function](/D/meas-fct) $X$ defined on a [probability space](/D/prob-spc) $(\Omega, \mathcal{E}, P)$ that maps from a [sample space](/D/samp-spc) $\Omega$ to the real numbers $\mathbb{R}$ using an [event space](/D/eve-spc) $\mathcal{E}$ and a [probability function](/D/dist) $P$;
 
 * more broadly, as any random quantity $X$ such as a [random event](/D/reve), a [random scalar](/D/rvar), a [random vector](/D/rvec) or a [random matrix](/D/rmat).

I/DbA.md

@@ -4,7 +4,7 @@ title: "Definition by Author"
 ---
 
 
-### JoramSoch (159 definitions)
+### JoramSoch (162 definitions)
 
 - [Akaike information criterion](/D/aic)
 - [Alternative hypothesis](/D/h1)
@@ -48,6 +48,7 @@ title: "Definition by Author"
 - [Empirical Bayesian log model evidence](/D/eblme)
 - [Empirical and theoretical prior distribution](/D/prior-emp)
 - [Estimation matrix](/D/emat)
+- [Event space](/D/eve-spc)
 - [Exceedance probability](/D/prob-exc)
 - [Expected value](/D/mean)
 - [Expected value of a random matrix](/D/mean-rmat)
@@ -119,6 +120,7 @@ title: "Definition by Author"
 - [Probability density function](/D/pdf)
 - [Probability distribution](/D/dist)
 - [Probability mass function](/D/pmf)
+- [Probability space](/D/prob-spc)
 - [Probability-generating function](/D/pgf)
 - [Projection matrix](/D/pmat)
 - [Quantile function](/D/qf)
@@ -135,6 +137,7 @@ title: "Definition by Author"
 - [Residual-forming matrix](/D/rfmat)
 - [Sample covariance matrix](/D/covmat-samp)
 - [Sample mean](/D/mean-samp)
+- [Sample space](/D/samp-spc)
 - [Sample variance](/D/var-samp)
 - [Sampling distribution](/D/dist-samp)
 - [Shannon entropy](/D/ent)

I/DbN.md

@@ -171,3 +171,6 @@ title: "Definition by Number"
 | D162 | cfm | [Corresponding forward model](/D/cfm) | JoramSoch | 2021-10-21 |
 | D163 | slr | [Simple linear regression](/D/slr) | JoramSoch | 2021-10-27 |
 | D164 | regline | [Regression line](/D/regline) | JoramSoch | 2021-10-27 |
+| D165 | samp-spc | [Sample space](/D/samp-spc) | JoramSoch | 2021-11-26 |
+| D166 | eve-spc | [Event space](/D/eve-spc) | JoramSoch | 2021-11-26 |
+| D167 | prob-spc | [Probability space](/D/prob-spc) | JoramSoch | 2021-11-26 |

I/DbT.md

@@ -64,6 +64,7 @@ title: "Definition by Topic"
 - [Empirical Bayesian log model evidence](/D/eblme)
 - [Encompassing model](/D/encm)
 - [Estimation matrix](/D/emat)
+- [Event space](/D/eve-spc)
 - [Exceedance probability](/D/prob-exc)
 - [Expected value](/D/mean)
 - [Expected value of a random matrix](/D/mean-rmat)
@@ -166,6 +167,7 @@ title: "Definition by Topic"
 - [Probability density function](/D/pdf)
 - [Probability distribution](/D/dist)
 - [Probability mass function](/D/pmf)
+- [Probability space](/D/prob-spc)
 - [Probability-generating function](/D/pgf)
 - [Projection matrix](/D/pmat)
 
@@ -192,6 +194,7 @@ title: "Definition by Topic"
 - [Sample covariance](/D/cov-samp)
 - [Sample covariance matrix](/D/covmat-samp)
 - [Sample mean](/D/mean-samp)
+- [Sample space](/D/samp-spc)
 - [Sample variance](/D/var-samp)
 - [Sampling distribution](/D/dist-samp)
 - [Shannon entropy](/D/ent)

I/PbA.md

@@ -4,7 +4,7 @@ title: "Proof by Author"
 ---
 
 
-### JoramSoch (280 proofs)
+### JoramSoch (283 proofs)
 
 - [(Non-)Multiplicativity of the expected value](/P/mean-mult)
 - [Accuracy and complexity for the univariate Gaussian](/P/ug-anc)
@@ -94,7 +94,10 @@ title: "Proof by Author"
 - [Kullback-Leibler divergence for the normal distribution](/P/norm-kl)
 - [Kullback-Leibler divergence for the normal-gamma distribution](/P/ng-kl)
 - [Law of the unconscious statistician](/P/mean-lotus)
+- [Law of total covariance](/P/cov-tot)
+- [Law of total expectation](/P/mean-tot)
 - [Law of total probability](/P/prob-tot)
+- [Law of total variance](/P/var-tot)
 - [Linear combination of independent normal random variables](/P/norm-lincomb)
 - [Linear transformation theorem for the matrix-normal distribution](/P/matn-ltt)
 - [Linear transformation theorem for the moment-generating function](/P/mgf-ltt)

I/PbN.md

@@ -296,3 +296,6 @@ title: "Proof by Number"
 | P288 | slr-ols2 | [Ordinary least squares for simple linear regression](/P/slr-ols2) | JoramSoch | 2021-11-16 |
 | P289 | slr-wls2 | [Weighted least squares for simple linear regression](/P/slr-wls2) | JoramSoch | 2021-11-16 |
 | P290 | slr-mle2 | [Maximum likelihood estimation for simple linear regression](/P/slr-mle2) | JoramSoch | 2021-11-16 |
+| P291 | mean-tot | [Law of total expectation](/P/mean-tot) | JoramSoch | 2021-11-26 |
+| P292 | var-tot | [Law of total variance](/P/var-tot) | JoramSoch | 2021-11-26 |
+| P293 | cov-tot | [Law of total covariance](/P/cov-tot) | JoramSoch | 2021-11-26 |

I/PbT.md

@@ -125,7 +125,10 @@ title: "Proof by Topic"
 ### L
 
 - [Law of the unconscious statistician](/P/mean-lotus)
+- [Law of total covariance](/P/cov-tot)
+- [Law of total expectation](/P/mean-tot)
 - [Law of total probability](/P/prob-tot)
+- [Law of total variance](/P/var-tot)
 - [Linear combination of independent normal random variables](/P/norm-lincomb)
 - [Linear transformation theorem for the matrix-normal distribution](/P/matn-ltt)
 - [Linear transformation theorem for the moment-generating function](/P/mgf-ltt)