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Home » Question: A fish population in a polluted lake is modeled by the function - Appcentric

Question: A fish population in a polluted lake is modeled by the function - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 #### 90.55

📌 ### Frage 7

📌 Ein Datenwissenschaftler, der sich mit maschinellem Lernen beschäftigt, verwendet die Log-Verlust-Formel \( L = -\frac{1}{n} \sum_{i=1}^n \left[ y_i \log(\hat{y}_i) + (1 - y_i) \log(1 - \hat{y}_i) \right] \). Für eine einzelne Vorhersage, bei der \( y = 1 \) und \( \hat{y} = 0.8 \), wie groß ist der Verlust?

📌 Setze die Werte ein: \( L = -\left[ 1 \cdot \log(0.8) + 0 \cdot \log(0.2) \right] = -\log(0.8) \).

📌 Berechne \( \log(0.8) \approx -0.2231 \), also \( L \approx 0.2231 \).

📌 #### 0.2231

📌 ### Frage 8

📌 Ein Biomedizinischer Ingenieur modelliert die Spannungskonzentration \( S \) an einem Implantat als \( S = \frac{2 \gamma}{\pi a} \), wobei \( \gamma = 50 \) MPa und \( a \) der Rissradius in mm ist. Wenn die maximal zulässige Spannung 20 MPa beträgt, wie groß ist der maximale zulässige Rissradius?

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