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Home » Since there are 5 values (odd), the median is the middle one: - inBeat

Since there are 5 values (odd), the median is the middle one: - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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We want $ \mathbb{E}[\text{output}] $.
Since $x$ is integer from 0 to 8, define indicator for each possible $...
Let $E = \sum_{k=0}^{8} \left( \text{output}(k) \cdot \mathbb{P}(x = k...
$\mathbb{P}(x = k) = \binom{8}{k} \left(\frac{1}{2}\right)^8 = \frac{\...
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 $

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