
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 5th, 2018, 01:01 AM  #1 
Senior Member Joined: Nov 2011 Posts: 230 Thanks: 2  Statistics Theorems
Which is the statistics theorem that is the most important in statistics?

May 5th, 2018, 04:06 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
I would say that it is the "Central Limit Theorem". It says that the average of a large number of independent trials, from any probability distribution with mean $\displaystyle \mu$ and standard deviation $\displaystyle \sigma$ will follow, approximately, the Normal Distribution with mean $\displaystyle \mu$ and standard deviation $\displaystyle \sigma$. A variant say that the sum of n trials from any probability distribution with mean $\displaystyle \mu$ and standard deviation $\displaystyle \sigma$ will follow, approximately, the Normal Distribution with mean $\displaystyle n\mu$ and standard deviation $\displaystyle \sqrt{n}\sigma$. That is the reason the normal distribution is so important. We can, for example, think of, say, the probability that each person in a large population will contract a given disease as following the same, unknown, probability distribution so we can, with confidence, use the normal distribution for the entire population.

May 5th, 2018, 08:39 AM  #3  
Senior Member Joined: Oct 2009 Posts: 555 Thanks: 179  Quote:
That is the most important theorem from frequentist statistics. It plays absolutely no role in Bayesian statistics.  

Tags 
statistics, theorems 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Integral theorems  chrishaig  Real Analysis  5  July 9th, 2013 01:00 PM 
Book of theorems  honzik  Math Books  1  November 13th, 2012 10:27 AM 
Gödel's Theorems  mrtamborineman10  Number Theory  7  August 9th, 2011 12:24 AM 
best introduction to statistics book? not applied statistics  ElMarsh  Advanced Statistics  2  October 23rd, 2009 05:10 PM 
Integral theorems  chrishaig  Calculus  0  December 31st, 1969 04:00 PM 