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Fix errors found by students

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This commit is contained in:
Andreas Tsouchlos 2025-12-11 13:11:29 +01:00
parent b06b64739f
commit aa9dab9491
1 changed files with 5 additions and 5 deletions
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10
src/2025-12-05/presentation.tex
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@ -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}