cleaning typos

doc/src/week36/week36.do.txt

@@ -1474,14 +1474,14 @@ We can, based on our discussions of the variance of $\bm{\beta}$ and the mean va
 
 !bt
 \[
-p(\bm{\beta})=\prod_{j=0}^{p-1}\exp{-(\frac{\beta_j^2}{2\tau^2}}.
+p(\bm{\beta})=\prod_{j=0}^{p-1}\exp{\left(-\frac{\beta_j^2}{2\tau^2}\right)}.
 \]
 !et
 
 Our posterior probability becomes then (omitting the normalization factor which is just a constant)
 !bt
 \[
-p(\bm{\beta}=\prod_{i=0}^{n-1}\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\bm{X}_{i,*}\bm{\beta})^2}{2\sigma^2}\right]}\prod_{j=0}^{p-1}\exp{-(\frac{\beta_j^2}{2\tau^2}}.
+p(\bm{\beta}=\prod_{i=0}^{n-1}\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\bm{X}_{i,*}\bm{\beta})^2}{2\sigma^2}\right]}\prod_{j=0}^{p-1}\exp{\left(-\frac{\beta_j^2}{2\tau^2}\right)}.
 \]
 !et
 
@@ -1494,7 +1494,7 @@ constants terms that do not depend on $\beta$, we have
 
 !bt
 \[
-C(\bm{\beta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\bm{y}-\bm{X}\bm{\beta})\vert\vert_2^2}{2\sigma^2}+\frac{1}{2\tau^2}\vert\vert\bm{\beta}\vert\vert_2^2,
+C(\bm{\beta}=\frac{\vert\vert (\bm{y}-\bm{X}\bm{\beta})\vert\vert_2^2}{2\sigma^2}+\frac{1}{2\tau^2}\vert\vert\bm{\beta}\vert\vert_2^2,
 \]
 !et
 and replacing $1/2\tau^2$ with $\lambda$ we have
@@ -1513,14 +1513,14 @@ To derive the Lasso cost function, we simply replace the Gaussian prior with an
 
 !bt
 \[
-p(\bm{\beta})=\prod_{j=0}^{p-1}\exp{-(\frac{\vert\beta_j\vert}{\tau}}.
+p(\bm{\beta})=\prod_{j=0}^{p-1}\exp{\left(-\frac{\vert\beta_j\vert}{\tau}\right)}.
 \]
 !et
 
 Our posterior probability becomes then (omitting the normalization factor which is just a constant)
 !bt
 \[
-p(\bm{\beta}=\prod_{i=0}^{n-1}\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\bm{X}_{i,*}\bm{\beta})^2}{2\sigma^2}\right]}\prod_{j=0}^{p-1}\exp{-(\frac{\vert\beta_j\vert}{\tau}}.
+p(\bm{\beta}=\prod_{i=0}^{n-1}\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\bm{X}_{i,*}\bm{\beta})^2}{2\sigma^2}\right]}\prod_{j=0}^{p-1}\exp{\left(-\frac{\vert\beta_j\vert}{\tau}\right)}.
 \]
 !et
 
@@ -1532,7 +1532,7 @@ constants terms that do not depend on $\beta$, we have
 
 !bt
 \[
-C(\bm{\beta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\bm{y}-\bm{X}\bm{\beta})\vert\vert_2^2}{2\sigma^2}+\frac{1}{\tau}\vert\vert\bm{\beta}\vert\vert_1,
+C(\bm{\beta}=\frac{\vert\vert (\bm{y}-\bm{X}\bm{\beta})\vert\vert_2^2}{2\sigma^2}+\frac{1}{\tau}\vert\vert\bm{\beta}\vert\vert_1,
 \]
 !et
 and replacing $1/\tau$ with $\lambda$ we have