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Insert pause in solution to exercise 1a

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Andreas Tsouchlos 2026-01-14 00:19:06 +01:00
parent a4df0108de
commit ddd70cae86
1 changed files with 4 additions and 1 deletions
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src/2026-01-16/presentation.tex
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@ -147,7 +147,10 @@
\pause\begin{align*} \pause\begin{align*}
P_Z(n) &= P_{X+Y}(n) = \nsum_{k=0}^{n} P_X(k)P_Y(n-k) P_Z(n) &= P_{X+Y}(n) = \nsum_{k=0}^{n} P_X(k)P_Y(n-k)
= \nsum_{k=0}^{n} \frac{\lambda_1^k \cdot e^{-\lambda_1}}{k!} = \nsum_{k=0}^{n} \frac{\lambda_1^k \cdot e^{-\lambda_1}}{k!}
\cdot \frac{\lambda_2^{n-k} \cdot e^{-\lambda_2}}{(n-k)!} \\[1mm] \cdot \frac{\lambda_2^{n-k} \cdot e^{-\lambda_2}}{(n-k)!}
\end{align*}
\vspace*{-4mm}
\pause\begin{align*}
&= e^{-(\lambda_1 + \lambda_2)} \nsum_{k=0}^{n} &= e^{-(\lambda_1 + \lambda_2)} \nsum_{k=0}^{n}
\frac{1}{k! (n-k)!} \lambda_1^k \lambda_2^{n-k} \\[3mm] \frac{1}{k! (n-k)!} \lambda_1^k \lambda_2^{n-k} \\[3mm]
&= \frac{e^{-(\lambda_1 + \lambda_2)}}{n!} \nsum_{k=0}^{n} &= \frac{e^{-(\lambda_1 + \lambda_2)}}{n!} \nsum_{k=0}^{n}