maths.free › Probability Theory › Applying Probability to Combinatorics › Estimating Ramsey Numbers
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: \[\begin{aligned}\end{aligned}\]
አሁን ምንም ዓይነት መሳሪያ ይህን አይቆጣጠርም፤ ነገር ግን ክፍሎቹ ሊቆጠሩ ይችላሉ። በታች ያለውን ይሞክሩ ወይም የራሳችሁን ይጻፉ።
ፊደላት
ለሙሉ መግለጫ፣ ምስል፣ እና በውስጡ ያለውን ፊደል ትርጓሜ ለማየት ማንኛውንም ምልክት ይጫኑ።
ጥያቄዎች
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.
የዚህ ገጽ ክፍሎች ከ Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0). እዚህ የተቀረጸና የተተረጎመ፤ ስህተቶች የእኛ ናቸው፡፡
በ Probability Theory
Sample spaces and the axiomsRandom variables and expectationThe common distributionsThe law of large numbers and the central limit theorem