Merge pull request #153 from StatProofBook/master

update to master

Author: JoramSoch

I/DbA.md

@@ -13,7 +13,7 @@ title: "Definition by Author"
 
 - [Sample covariance](/D/cov-samp)
 
-### JoramSoch (188 definitions)
+### JoramSoch (189 definitions)
 
 - [Akaike information criterion](/D/aic)
 - [Alternative hypothesis](/D/h1)
@@ -184,6 +184,7 @@ title: "Definition by Author"
 - [Standard normal distribution](/D/snorm)
 - [Standard uniform distribution](/D/suni)
 - [Standardized moment](/D/mom-stand)
+- [Statistic](/D/stat)
 - [Statistical hypothesis](/D/hyp)
 - [Statistical hypothesis test](/D/test)
 - [Statistical independence](/D/ind)

I/DbN.md

@@ -211,3 +211,4 @@ title: "Definition by Number"
 | D202 | prior-pred | [Prior predictive distribution](/D/prior-pred) | aloctavodia | 2024-08-19 |
 | D203 | data | [Data](/D/data) | JoramSoch | 2024-09-20 |
 | D204 | para | [Parameter](/D/para) | JoramSoch | 2024-09-27 |
+| D205 | stat | [Statistic](/D/stat) | JoramSoch | 2024-10-04 |

I/DbT.md

@@ -241,6 +241,7 @@ title: "Definition by Topic"
 - [Standard normal distribution](/D/snorm)
 - [Standard uniform distribution](/D/suni)
 - [Standardized moment](/D/mom-stand)
+- [Statistic](/D/stat)
 - [Statistical hypothesis](/D/hyp)
 - [Statistical hypothesis test](/D/test)
 - [Statistical independence](/D/ind)

I/PbA.md

@@ -12,7 +12,7 @@ title: "Proof by Author"
 
 - [Posterior predictive distribution is a marginal distribution of the joint likelihood](/P/postpred-jl)
 
-### JoramSoch (436 proofs)
+### JoramSoch (437 proofs)
 
 - [Accuracy and complexity for Bayesian linear regression](/P/blr-anc)
 - [Accuracy and complexity for Bayesian linear regression with known covariance](/P/blrkc-anc)
@@ -270,6 +270,7 @@ title: "Proof by Author"
 - [Normal distribution is a special case of multivariate normal distribution](/P/norm-mvn)
 - [Normal distribution maximizes differential entropy for fixed variance](/P/norm-maxent)
 - [Normal-gamma distribution is a special case of normal-Wishart distribution](/P/ng-nw)
+- [Normally distributed and uncorrelated does not imply independent](/P/norm-corrind)
 - [Omnibus F-test for multiple regressors in multiple linear regression](/P/mlr-fomnibus)
 - [One-sample t-test for independent observations](/P/ug-ttest1)
 - [One-sample z-test for independent observations](/P/ugkv-ztest1)

I/PbN.md

@@ -478,3 +478,4 @@ title: "Proof by Number"
 | P470 | ind-self | [Self-independence of random event](/P/ind-self) | JoramSoch | 2024-09-20 |
 | P471 | med-mae | [The median minimizes the mean absolute error](/P/med-mae) | salbalkus | 2024-09-23 |
 | P472 | corr-ind | [Independent random variables are uncorrelated](/P/corr-ind) | JoramSoch | 2024-09-27 |
+| P473 | norm-corrind | [Normally distributed and uncorrelated does not imply independent](/P/norm-corrind) | JoramSoch | 2024-10-04 |

I/PbT.md

@@ -315,6 +315,7 @@ title: "Proof by Topic"
 - [Normal distribution is a special case of multivariate normal distribution](/P/norm-mvn)
 - [Normal distribution maximizes differential entropy for fixed variance](/P/norm-maxent)
 - [Normal-gamma distribution is a special case of normal-Wishart distribution](/P/ng-nw)
+- [Normally distributed and uncorrelated does not imply independent](/P/norm-corrind)
 
 ### O
 

I/ToC.md

@@ -483,7 +483,7 @@ title: "Table of Contents"
    &emsp;&ensp; 3.2.24. **[Kullback-Leibler divergence](/P/norm-kl)** <br>
    &emsp;&ensp; 3.2.25. **[Maximum entropy distribution](/P/norm-maxent)** <br>
    &emsp;&ensp; 3.2.26. **[Linear combination of independent normals](/P/norm-lincomb)** <br>
-   &emsp;&ensp; 3.2.27. **[Normal and uncorrelated does not imply independent](/P/norm-indcorr)** <br>
+   &emsp;&ensp; 3.2.27. **[Normal and uncorrelated does not imply independent](/P/norm-corrind)** <br>
 
    <p id="t-distribution"></p>
    3.3. t-distribution <br>

P/norm-corrind.md

@@ -47,7 +47,7 @@ p(V=0)  = p(V=1)  = \frac{1}{2}
 p(W=-1) = p(W=+1) = \frac{1}{2} \; .
 $$
 
-Moreover, let $X$ follow a [standard normal distribution](/D/snorm) and let $Y$ be defined as a transformation of $X$ and $W$:
+Moreover, let $X$ follow a [standard normal distribution](/D/snorm) and let $Y$ be defined as a combination of $X$ and $W$:
 
 $$ \label{eq:X-Y}
 \begin{split}

P/norm-lincomb.md

@@ -11,7 +11,7 @@ title: "Linear combination of independent normal random variables"
 chapter: "Probability Distributions"
 section: "Univariate continuous distributions"
 topic: "Normal distribution"
-theorem: "Linear combination"
+theorem: "Linear combination of independent normals"
 
 sources: