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Estimating Ramsey Numbers
We will find it convenient to utilize the following approximation due to Stirling. You can find a proof in almost any advanced calculus book.
Estimating Ramsey Numbers
We will find it convenient to utilize the following approximation due to Stirling. You can find a proof in almost any advanced calculus book. \[\begin{aligned}\end{aligned}\] Of course, we will normally be satisfied with the first term: \[\begin{aligned}\end{aligned}\] Using Stirling's approximation and the binomial coefficients from the proof of , we have the following upper bound: \[\begin{aligned}\end{aligned}\]
今度はあなたの番 計算機では解けませんが、計算可能です。下の一つを試してみましょう。もしくは自分で入力してください。
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よくある質問
What is the difference between probability and statistics?
Probability goes from a known model to what the data should look like; statistics goes from data back to the model. Probability theory is the deductive half.
What does the law of large numbers promise?
That the average of many independent samples converges to the expected value. It says nothing about any single trial.
Parts of this page are adapted from Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0). ここでは要約して説明し直しています。誤りは私たちの責任です。
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Sample spaces and the axiomsRandom variables and expectationThe common distributionsThe law of large numbers and the central limit theorem