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Home » $ z \overlinew + \overlinez w = 10 $ - jntua results

$ z \overlinew + \overlinez w = 10 $ - jntua results

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Hence, the probability that exactly 3 projects are Exceptionally Strong is:

📌 \binom{7}{3} \cdot 0^3 \cdot (1 - 0)^4 = 0

📌 Thus, the probability is $\boxed{0}$.

📌 Question: A robotics engineer is testing a robot that moves on a grid, making exactly 8 steps from the origin $(0,0)$ to some point $(x,y)$, with each step either increasing $x$ by 1 or $y$ by 1. The robot must end at a point where $x + y = 8$, $x \geq 3$, and output $x$ if $x \geq 4$, or $y$ if $x < 4$. What is the expected value of the output?

📌 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: $x \sim \text{Binomial}(8, \frac{1}{2})$.

📌 The robot outputs:

📌 $x$, if $x \geq 4$,

📌 $y = 8 - x$, if $x < 4$.

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