corrected some pages

Several small mistakes/errors were corrected in several proofs/definitions.

Author: JoramSoch

P/covmat-sum.md

@@ -7,7 +7,7 @@ affiliation: "BCCN Berlin"
 e_mail: "joram.soch@bccn-berlin.de"
 date: 2022-09-26 10:37:00
 
-title: "Covariance of the sum of two random vectors"
+title: "Covariance matrix of the sum of two random vectors"
 chapter: "General Theorems"
 section: "Probability theory"
 topic: "Covariance"

P/f-pdf.md

@@ -94,7 +94,7 @@ $$ \label{eq:f-XY}
 f_{X,Y}(x,y) = f_X(x) \cdot f_Y(y) \; .
 $$
 
-With the [probability density function of an invertible function](/P/pdf-invfct), the [joint density](/D/dist-joint) of $T$ and $W$ can be derived as:
+With the [probability density function of an invertible function](/P/pdf-invfct), the [joint density](/D/dist-joint) of $F$ and $W$ can be derived as:
 
 $$ \label{eq:f-FW-s1}
 f_{F,W}(f,w) = f_{X,Y}(x,y) \cdot \lvert J \rvert \; .

P/lognorm-mean.md

@@ -84,7 +84,7 @@ $$
 and, with unit variance $\sigma^2 = 1$, this reads:
 
 $$
-= \frac{1}{\sqrt{2 \pi}} \cdot \exp \left[ -\frac{1}{2} \left({x-\mu} \right)^2 \right]
+f_X(x) = \frac{1}{\sqrt{2 \pi}} \cdot \exp \left[ -\frac{1}{2} \left({x-\mu} \right)^2 \right]
 $$
 
 Using the definition of the [probability density function](/D/pdf), we get

P/lognorm-var.md

@@ -103,7 +103,7 @@ $$
 and, with $\mu = 2 \sigma$ and unit variance, this reads:
 
 $$ 
-= \frac{1}{\sqrt{2 \pi}} \cdot \exp \left[ -\frac{1}{2} \left({x - 2 \sigma} \right)^2 \right] \; .
+f_X(x) = \frac{1}{\sqrt{2 \pi}} \cdot \exp \left[ -\frac{1}{2} \left({x - 2 \sigma} \right)^2 \right] \; .
 $$
 
 Using the definition of the [probability density function](/D/pdf), we get