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Omni-MATH / Let x₀=x₁₀₁=0. The numbers x₁,x₂,…,x₁₀₀ are chosen at random from the interval [0,1] uniformly and independently. Compute the probability that 2x_(i)≥x_(i−1)+x_(i+1) for all …

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problem

Let x0=x101=0x_{0}=x_{101}=0. The numbers x1,x2,…,x100x_{1}, x_{2}, \ldots, x_{100} are chosen at random from the interval [0,1][0,1] uniformly and independently. Compute the probability that 2xi≥xi−1+xi+12 x_{i} \geq x_{i-1}+x_{i+1} for all i=1,2,…i=1,2, \ldots, 100.
Plain-text mathematical notation (without MathML)
Let x₀=x₁₀₁=0. The numbers x₁,x₂,…,x₁₀₀ are chosen at random from the interval [0,1] uniformly and independently. Compute the probability that 2x_(i)≥x_(i−1)+x_(i+1) for all i=1,2,…, 100.
Original LaTeX notation
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.

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Source and history

task_id
56d49862-4a0b-5323-abc6-e5c7bb85f975
task_key
test--56d49862-4a0b-5323-abc6-e5c7bb85f975
task_revision_id
1
config / split
/ test

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