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Probability Theory

Random variables, distributions, expectation, limit theorems.

பாடங்கள்

Introductory Sample spaces and the axioms Kolmogorov's axioms, events as sets, conditional probability and Bayes. 1 - (5/6)^4 Core Random variables and expectation Distributions, expected value, variance, linearity of expectation. 10 * 1/2 Core The common distributions Bernoulli, binomial, Poisson, uniform, exponential, normal, and what each models. integrate e^(-x^2/2)/sqrt(2*pi) dx from -1.96 to 1.96 Advanced The law of large numbers and the central limit theorem Why averages converge and why they are normally distributed. limit of (1 + 1/n)^n as n -> oo

Statistics measures data; probability theory is the mathematics underneath it. Distributions as functions, expectation as an integral, and the laws that make averages settle down.

மேலும் பாடங்கள்

Probability

An Introduction to Probability Conditional Probability and Independent Events Bernoulli Trials Discrete Random Variables Central Tendency Probability Spaces with Infinitely Many Outcomes Discussion

Applying Probability to Combinatorics

A First Taste of Ramsey Theory Small Ramsey Numbers Estimating Ramsey Numbers Applying Probability to Ramsey Theory Ramsey's Theorem The Probabilistic Method Discussion

Foundations

Probability theory Probability space Probability axioms Conditional probability Bayes' theorem Independence (probability theory)Random variable Probability distribution Cumulative distribution function Probability density function

Distributions

Binomial distribution Poisson distribution Normal distribution Exponential distribution Uniform distribution (continuous)Geometric distribution Chi-squared distribution Student's t-distribution

Limit theorems

Expected value Variance Covariance Law of large numbers Central limit theorem Chebyshev's inequality Moment-generating function Convergence of random variables Markov chain Martingale (probability theory)Stochastic process Brownian motion

இந்த பாடங்களில் சில திறந்த உரையிலிருந்து மாற்றப்பட்டுள்ளன: Keller & Trotter, Applied Combinatorics, Wikipedia. ஒவ்வொரு பாடப் பக்கமும் அதன் மூலத்தையும் உரிமத்தையும் குறிப்பிடுகிறது.

இங்கே பயன்படுத்தப்பட்ட குறியீடுகள்

முழுமையான வரையறை, ஒரு படத்தை, மற்றும் ஒவ்வொரு எழுத்தும் என்ன அர்த்தம் என்று எந்த சின்னத்தையும் அழுத்து.

கேள்விகள்

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.

உங்கள் சொந்த பிரச்சனை உள்ளது?
தீர்ப்பாளர் பக்கத்தில் அதை எழுதவும் அல்லது வரையவும்: ஒவ்வொரு படியும், ஒரு படமாக, நீங்கள் கேட்கும் வரை பதில் மறைக்கப்படும். தீர்வு →

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