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📰 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: 📰 This Biryani Taste Like Homeeat It Now Before Someone Else Does 9056482 📰 From Lap Companions To Playmates Why Medium Size Dogs Are Perfect For Your Home 1148068 📰 Shooting At Portland Oregon 9983971 📰 Microsoft Xbox Game Pass Ultimate 7454621 📰 Games Download For Laptop Free 6452308 📰 Can You Survive The Papa Game See The Epic Fails Thatll Make You Gasps 8153903 📰 Ppf Economics 5580642 📰 A Call From The Depths 3573766 📰 Dre Meaning 7572617 📰 Calculo Hipoteca 8736321 📰 Fourkites The Secret Hack Every Creator Needs To Skyrocket Engagement 2865951 📰 What Are Helocs 7152988 📰 You Wont Believe How Iconic Each Jurassic Park Character Changed Cinema Forever 5861529 📰 First Home Buyer Program 9488923 📰 Can I Withdraw Cash From My Credit Card 9376017