update sources from lecture-python (8e20ffa) using tomyst (b06cacb)

Author: mmcky

lectures/exchangeable.md

@@ -116,10 +116,10 @@ $$
 Using the laws of probability, we can always factor such a joint density into a product of conditional densities:
 
 $$
-\begin{align}
+\begin{aligned}
   p(W_T, W_{T-1}, \ldots, W_1, W_0)    = & p(W_T | W_{T-1}, \ldots, W_0) p(W_{T-1} | W_{T-2}, \ldots, W_0) \cdots  \cr
   & \quad \quad \cdots p(W_1 | W_0) p(W_0)
-\end{align}
+\end{aligned}
 $$
 
 In general,

lectures/harrison_kreps.md

@@ -195,8 +195,8 @@ Temporarily pessimistic believe the transition matrix
 $$
 P_p =
     \begin{bmatrix}
-        \frac{1}{2} & \frac{1}{2} \\
-        \frac{1}{4} & \frac{3}{4}
+        \frac{2}{3} & \frac{1}{3} \\
+        \frac{2}{3} & \frac{1}{3}
     \end{bmatrix}
 $$
 

lectures/lq_inventories.md

@@ -141,8 +141,7 @@ To form the matrices $R, Q, N$ in an LQ dynamic programming problem, we note tha
 time $t$ function can be expressed
 
 $$
-\begin{equation}
-\begin{split}
+\begin{aligned}
 \pi_{t} =&p_{t}S_{t}-c\left(Q_{t}\right)-d\left(I_{t},S_{t}\right)  \\
     =&\left(a_{0}-a_{1}S_{t}+v_{t}\right)S_{t}-c_{1}Q_{t}-c_{2}Q_{t}^{2}-d_{1}I_{t}-d_{2}\left(S_{t}-I_{t}\right)^{2}  \\
     =&a_{0}S_{t}-a_{1}S_{t}^{2}+Gz_{t}S_{t}-c_{1}Q_{t}-c_{2}Q_{t}^{2}-d_{1}I_{t}-d_{2}S_{t}^{2}-d_{2}I_{t}^{2}+2d_{2}S_{t}I_{t}  \\
@@ -170,8 +169,7 @@ Q_{t} & S_{t}\end{array}\right]\underset{\equiv N}{\underbrace{\left[\begin{arra
 I_{t}\\
 z_{t}
 \end{array}\right]\right)
-\end{split}
-\end{equation}
+\end{aligned}
 $$
 
 where $S_{c}=\left[1,0\right]$.

lectures/lqcontrol.md

@@ -563,7 +563,7 @@ In the module, the various updating, simulation and fixed point methods
 are wrapped in a class  called `LQ`, which includes
 
 * Instance data:
-    * The required parameters $Q, R, A, B$ and optional parameters C, β, T, R_f, N specifying a given LQ model
+    * The required parameters $Q, R, A, B$ and optional parameters $C, \beta, T, R_f, N$ specifying a given LQ model
         * set $T$ and $R_f$ to `None` in the infinite horizon case
         * set `C = None` (or zero) in the deterministic case
     * the value function and policy data