SAMPLING DISTRIBUTION OF THE MEAN AND THE CENTRAL LIMIT THEOREM
Below is the Matlab code used to perform the application of the Central Limit Theorem
Finite-range dependence implies the mixing conditions that ensure the central limit theorem
in Equation (3).
Applications of the central limit theorem
exist in the gaming literature as well.
Laplace discovered that the means are distributed approximately according to the normal curve and the Central Limit Theorem
is sometimes known as the "normal law of random errors.
There has been much confusion in the insurance economics literature with regard to the implications of the law of large numbers and the central limit theorem
Lee (1996), The central limit theorem
for weighted minimal spanning trees on random points, Ann.
Note that without a numerical value for C, the result, while providing information about the rate of convergence in the central limit theorem
, does not provide an answer to the undergraduate question mentioned above.
In order to prove the central limit theorem
we go back to (2) and similarly expand the integral
Hwang, On convergence rates in the central limit theorems
for combinatorial structures, European J.
Working from the assumption readers have completed a first- or second-year undergraduate course in analysis, which included some work in measure theory, Lesigne covers modeling an experiment in probability, random variables, independence, binomial distribution, the strong and weak laws of large numbers, the large deviation estimate, the central limit theorem
, the moderate deviations estimate, the local limit theorem, the arcsine law, the law of iterated logarithm, and the recurrence of random walks.
Generating Functions and the Central Limit Theorem