Skip to content

Commit 95bbd60

Browse files
committed
corrected some pages
Several small corrections were done to several proofs and definitions.
1 parent d52d1ab commit 95bbd60

2 files changed

Lines changed: 2 additions & 2 deletions

File tree

P/bvn-pdf.md

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -40,7 +40,7 @@ $$ \label{eq:mvn-pdf}
4040
f_X(x) = \frac{1}{\sqrt{(2 \pi)^n |\Sigma|}} \cdot \exp \left[ -\frac{1}{2} (x-\mu)^\mathrm{T} \Sigma^{-1} (x-\mu) \right] \; .
4141
$$
4242

43-
Plugging in $n = 2$, $\mu = \left[ \begin{matrix} \mu_1 \\\\ \mu_2 \end{matrix} \right]$ and $\Sigma = \left[ \begin{matrix} \sigma_1^2 \& \sigma_{12} \\\\ \sigma_{12} \& \sigma_2^2 \end{matrix} \right]$, we obtain:
43+
Plugging in $n = 2$, $\mu = \left[ \begin{matrix} \mu_1 \\\\ \mu_2 \end{matrix} \right]$ and $\Sigma = \left[ \begin{matrix} \sigma_1^2 & \sigma_{12} \\\\ \sigma_{12} & \sigma_2^2 \end{matrix} \right]$, we obtain:
4444

4545
$$ \label{eq:bvn-pdf-s1}
4646
\begin{split}

P/bvn-pdfcorr.md

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -42,7 +42,7 @@ $$
4242
where $\rho$ is the [correlation](/D/corr) between $X_1$ and $X_2$.
4343

4444

45-
**Proof:** Since $X$ follows a special case of the [multivariate normal distribution, its covariance matrix is](/P/mvn-corr)
45+
**Proof:** Since $X$ follows a special case of the [multivariate normal distribution, its covariance matrix is](/P/mvn-cov)
4646

4747
$$ \label{eq:cov-X}
4848
\mathrm{Cov}(X) = \Sigma = \left[ \begin{matrix} \sigma_1^2 & \sigma_{12} \\ \sigma_{12} & \sigma_2^2 \end{matrix} \right]

0 commit comments

Comments
 (0)