updated index pages

The index pages were updated with the recently added proofs.

Author: JoramSoch

I/PbA.md

@@ -8,7 +8,7 @@ title: "Proof by Author"
 
 - [Covariance matrix of the multinomial distribution](/P/mult-cov)
 
-### JoramSoch (398 proofs)
+### JoramSoch (399 proofs)
 
 - [Accuracy and complexity for the univariate Gaussian](/P/ug-anc)
 - [Accuracy and complexity for the univariate Gaussian with known variance](/P/ugkv-anc)
@@ -229,6 +229,7 @@ title: "Proof by Author"
 - [Moment-generating function of the normal distribution](/P/norm-mgf)
 - [Monotonicity of probability](/P/prob-mon)
 - [Monotonicity of the expected value](/P/mean-mono)
+- [Multinomial test](/P/mult-test)
 - [Multiple linear regression is a special case of the general linear model](/P/mlr-glm)
 - [Multivariate normal distribution is a special case of matrix-normal distribution](/P/mvn-matn)
 - [Necessary and sufficient condition for independence of multivariate normal random variables](/P/mvn-ind)

I/PbN.md

@@ -435,3 +435,4 @@ title: "Proof by Number"
 | P427 | bin-map | [Maximum-a-posteriori estimation for binomial observations](/P/bin-map) | JoramSoch | 2023-12-01 |
 | P428 | mult-map | [Maximum-a-posteriori estimation for multinomial observations](/P/mult-map) | JoramSoch | 2023-12-08 |
 | P429 | bin-test | [Binomial test](/P/bin-test) | JoramSoch | 2023-12-16 |
+| P430 | mult-test | [Multinomial test](/P/mult-test) | JoramSoch | 2023-12-23 |

I/PbT.md

@@ -274,6 +274,7 @@ title: "Proof by Topic"
 - [Moments of the chi-squared distribution](/P/chi2-mom)
 - [Monotonicity of probability](/P/prob-mon)
 - [Monotonicity of the expected value](/P/mean-mono)
+- [Multinomial test](/P/mult-test)
 - [Multiple linear regression is a special case of the general linear model](/P/mlr-glm)
 - [Multivariate normal distribution is a special case of matrix-normal distribution](/P/mvn-matn)
 

P/mult-test.md

@@ -73,13 +73,13 @@ $$
 such that the probability of observing the counts $y$, given $H_0$, is
 
 $$ \label{eq:Pr0-y}
-\mathrm{Pr}(y \vert H_0) = n! \prod_{j=1}^k \frac{ {p_{0i}}^{y_j} }{y_j!} \; .
+\mathrm{Pr}(y \vert H_0) = n! \prod_{j=1}^k \frac{p_{0i}^{y_j}}{y_j!} \; .
 $$
 
 The probability of observing any other set of counts $x$, given $H_0$, is
 
 $$ \label{eq:Pr0-x}
-\mathrm{Pr}(x \vert H_0) = n! \prod_{j=1}^k \frac{ {p_{0i}}^{x_j} }{x_j!} \; .
+\mathrm{Pr}(x \vert H_0) = n! \prod_{j=1}^k \frac{p_{0i}^{x_j}}{x_j!} \; .
 $$
 
 The [p-value](/D/pval) is the probability of observing a value of the [test statistic](/D/tstat) that is as extreme or more extreme then the actually observed test statistic. Any set of counts $x$ might be considered as extreme or more extreme than the actually observed counts $y$, if the former is equally probable or less probably than the latter: