From ddd70cae864232c4a0569fc37f1c4c0923c54a0e Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Wed, 14 Jan 2026 00:19:06 +0100 Subject: [PATCH] Insert pause in solution to exercise 1a --- src/2026-01-16/presentation.tex | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/src/2026-01-16/presentation.tex b/src/2026-01-16/presentation.tex index 4c826be..61c768a 100644 --- a/src/2026-01-16/presentation.tex +++ b/src/2026-01-16/presentation.tex @@ -147,7 +147,10 @@ \pause\begin{align*} 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!} - \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} \frac{1}{k! (n-k)!} \lambda_1^k \lambda_2^{n-k} \\[3mm] &= \frac{e^{-(\lambda_1 + \lambda_2)}}{n!} \nsum_{k=0}^{n}