This week’s Fiddler is about rounding! Let $\text{round}(x)$ be the value of $x$ rounded to the nearest integer. Suppose $x_1,\dots,x_n$ are independent uniformly distributed random variables in $[0,1]$. Find the probability that \[ \text{round}(x_1+\cdots+x_n) = \text{round}(x_1)+\cdots+\text{round}(x_n) \] My solution: [Show Solution] Let’s call the probability we seek $p(n)$. The values of the $x_i$ determine what … Continue reading "Round, round, get a round" The post Round, round, ...
