Question 67
Let $x_{0} = x_{101} = 0$. The numbers $x_{1}, x_{2}, \ldots, x_{100}$ are chosen at random from the interval $[0,1]$ uniformly and independently. Compute the probability that $2 x_{i} \geq x_{i-1} + x_{i+1}$ for all $i = 1, 2, \ldots, 100$.