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17872 environment does not need align or split explicitly
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lectures/exchangeable.md

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@@ -116,10 +116,8 @@ $$
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Using the laws of probability, we can always factor such a joint density into a product of conditional densities:
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$$
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\begin{align}
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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
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& p(W_1 | W_0) p(W_0)
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\end{align}
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$$
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In general,

lectures/lq_inventories.md

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@@ -140,8 +140,6 @@ To form the matrices $R, Q, H$, we note that the firm’s profits at
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time $t$ function can be expressed
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$$
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\begin{equation}
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\begin{split}
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\pi_{t} =&p_{t}S_{t}-c\left(Q_{t}\right)-d\left(I_{t},S_{t}\right) \\
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=&\left(a_{0}-a_{1}S_{t}+v_{t}\right)S_{t}-c_{1}Q_{t}-c_{2}Q_{t}^{2}-d_{1}I_{t}-d_{2}\left(S_{t}-I_{t}\right)^{2} \\
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=&a_{0}S_{t}-a_{1}S_{t}^{2}+Gz_{t}S_{t}-c_{1}Q_{t}-c_{2}Q_{t}^{2}-d_{1}I_{t}-d_{2}S_{t}^{2}-d_{2}I_{t}^{2}+2d_{2}S_{t}I_{t} \\
@@ -168,8 +166,6 @@ Q_{t} & S_{t}\end{array}\right]\underset{\equiv N}{\underbrace{\left[\begin{arra
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I_{t}\\
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z_{t}
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\end{array}\right]\right)
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\end{split}
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\end{equation}
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$$
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where $S_{c}=\left[1,0\right]$.

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