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Wutz edited textbf_Aufgabe_2_p_i_X_1__.tex
over 8 years ago
Commit id: 234c0a5e609f69c78bc454381a424b6e58de7c25
deletions | additions
diff --git a/textbf_Aufgabe_2_p_i_X_1__.tex b/textbf_Aufgabe_2_p_i_X_1__.tex
index 1d76b28..8db833a 100644
--- a/textbf_Aufgabe_2_p_i_X_1__.tex
+++ b/textbf_Aufgabe_2_p_i_X_1__.tex
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$\Leftrightarrow\sum_{n\in\mathbb{N}}n*(1-e^{-\theta})*\frac{\theta^n}{n!}*e^{-\theta}*\frac{1}{1-e^{-\theta}}=\theta$\\
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$\Leftrightarrow
e^{-\theta}*\frac{1}{1-e^{-\theta}}*\sum_{n\in\mathbb{N}}n*(1-e^{-\theta})*\frac{\theta^n}{n!}=\theta$ e^{-\theta}*\frac{1}{1-e^{-\theta}}*\sum_{n\in\mathbb{N}}n*(1-e^{-\theta})*\frac{\theta^n}{n!}=\theta$\\
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$\Leftrightarrow e^{-\theta}*\sum_{n\in\mathbb{N}}n*\frac{\theta^n}{n!}=\theta$\\
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$\Leftrightarrow e^{-\theta}*\theta*\sum_{i=1}^{\infty}\frac{\theta^{n-1}}{(n-19!}=\theta$