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\( 5^3 = 125 \equiv 5 \) - AMAZONAWS
\( 5^3 = 125 \equiv 5 \) - AMAZONAWS
📅 March 6, 2026
👤 scraface
Mar 06, 2026
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📌 Solution: The robot takes 8 steps, each independently choosing to go right (increase $x$) or up (increase $y$), uniformly at random (assume fair walk). The endpoint is $(x, 8 - x)$ for $x = 0,1,\dots,8$, so $x$ follows a binomial distribution: $x \sim \text{Binomial}(8, \frac{1}{2})$.
📌 We want $ \mathbb{E}[\text{output}] $.