From aa9dab949148e85bae334502394f8a962a35dade Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Thu, 11 Dec 2025 13:11:29 +0100 Subject: [PATCH] Fix errors found by students --- src/2025-12-05/presentation.tex | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/src/2025-12-05/presentation.tex b/src/2025-12-05/presentation.tex index 3af4b85..7c59faa 100644 --- a/src/2025-12-05/presentation.tex +++ b/src/2025-12-05/presentation.tex @@ -284,7 +284,7 @@ X \sim \text{Bin}(N,p) \end{gather*} \begin{gather*} - P_X(k) = \binom{N}{k} p^k (1-p)^{1-k} + P_X(k) = \binom{N}{k} p^k (1-p)^{N-k} \end{gather*} \begin{align*} E(X) &= Np\\ @@ -338,7 +338,7 @@ \begin{greenblock}{Binomialverteilung} \vspace*{-6mm} \begin{gather*} - P_X(k) = \binom{N}{k} p^k (1-p)^{1-k} + P_X(k) = \binom{N}{k} p^k (1-p)^{N-k} \end{gather*} \begin{align*} E(X) &= Np\\ @@ -513,9 +513,9 @@ \end{gather*}% \vspace*{-14mm}% \begin{align*} - P(R = 0) &= P(A = 0 \text{ und } L = 0) &&\hspace{-24mm}= p_A\cdot p_L &&\hspace{-24mm}= 0{,}56 \\ + P(R = 0) &= P(A = 0 \text{ und } L = 0) &&\hspace{-24mm}= p_A\cdot p_L &&\hspace{-24mm}= 0{,}06 \\ P(R = 1) &= P(A=1 \text{ und } L=0) + P(A=0 \text{ und } L=1) &&\hspace{-24mm}= p_A \cdot (1-p_L) + (1-p_A)\cdot p_L &&\hspace{-24mm}= 0{,}38 \\ - P(R = 2) &= P(A=1 \text{ und } L=1) &&\hspace{-24mm}= (1-p_A)(1-p_L) &&\hspace{-24mm}= 0{,}06 + P(R = 2) &= P(A=1 \text{ und } L=1) &&\hspace{-24mm}= (1-p_A)(1-p_L) &&\hspace{-24mm}= 0{,}56 \end{align*} \vspace*{-10mm}\pause \item Der Autofahrer fährt an $200$ unabhängigen Tagen im Jahr über seinen Arbeitsweg zur Arbeit. Wie viele Strafzettel sammelt der @@ -665,7 +665,7 @@ \begin{greenblock}{Erzeugende Funktion} \vspace*{-6mm} \begin{gather*} - \psi(z) = \sum_{n=1}^{\infty} z^n P(x=n)\\[5mm] + \psi(z) = \sum_{n=1}^{\infty} z^n P(X=n)\\[5mm] P(X=n) = \frac{\psi_X^{(n)}(0)}{n!} \end{gather*} \end{greenblock}