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Home » Substitute \( x = 2 \) into the cost function: - AMAZONAWS

Substitute \( x = 2 \) into the cost function: - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 The robot outputs:

📌 $x$, if $x \geq 4$,

📌 $y = 8 - x$, if $x < 4$.

📌 We want $ \mathbb{E}[\text{output}] $.

📌 Since $x$ is integer from 0 to 8, define indicator for each possible $x$:

📌 Let $E = \sum_{k=0}^{8} \left( \text{output}(k) \cdot \mathbb{P}(x = k) \right)$

📌 $\mathbb{P}(x = k) = \binom{8}{k} \left(\frac{1}{2}\right)^8 = \frac{\binom{8}{k}}{256}$

📌 For $k = 0,1,2,3$: output = $y = 8 - k$

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