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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: \[\begin{aligned}\end{aligned}\]

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Àwọn Àtòjọ-ẹ̀yàn

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.

Àwọn ààyè ojú-ìwé yìí tí a fi pamọ́ láti Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0). Tí a fi pamọ́ síì níbẹ̀; àwọn àwọn àṣiṣe ní wa.

Diẹ̀ nínú Probability Theory

Sample spaces and the axioms Random variables and expectation The common distributions The law of large numbers and the central limit theorem