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Home » First, calculate the score for the 5th game: - Crosslake

First, calculate the score for the 5th game: - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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For $k = 0,1,2,3$: output = $y = 8 - k$
For $k = 4,5,6,7,8$: output = $k$
\mathbb{E}[\text{output}] = \sum_{k=0}^{3} (8 - k) \cdot \frac{\binom{...
Compute each sum.
First sum ($k = 0$ to $3$):
$ (8-0)\binom{8}{0} = 8 \cdot 1 = 8 $
$ (8-1)\binom{8}{1} = 7 \cdot 8 = 56 $
$ (8-2)\binom{8}{2} = 6 \cdot 28 = 168 $
$ (8-3)\binom{8}{3} = 5 \cdot 56 = 280 $
Total = $8 + 56 + 168 + 280 = 512$

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