Statistics 2
Section outline
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Mathematical Statistics is a branch of mathematics that deals with the development and application of statistical methods, focusing on the mathematical aspects of probability theory and statistical inference. It involves the study of various statistical models, their properties, and the development of mathematical techniques for analyzing and interpreting data.
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The content of stat2
Set theory : definition of sets, types of sets, set operations, set theory foemulats.
The first axis
Experiment and event : aleatoire event, random experiment, sample space, Event
The second axis
Combinatory analysis : the basic principale of counting, permutation, arrangements, combinations
The third axis
Probabilities : Probability theory (definition, probability cumpute ) , probability characteristics, independence, conditional probability, total theory probabity, Bays theory.
The fourth axis
· Random of discrete variables :
· Definition of random of variable, classification of random variables
· Probability distribution of discrete variables : Density function, Distribution function F(x).
· Other discrete distibution : (regular distribution, Bernoulli, Binomial, poisson…..)
The fifth axis
· Random of continuons variables
· Probability distribution of continuous variables :Probability Density function f(x), Distribution function F(x).
· Other continuous distibution : ( Normal distribution, distibution of the place gauss, …..)
The sixth axis
· Expected value E(X): definition and caracteristics
· Variance V(X): definition and caracteristics
The seventh axis
· The Moment
· Moment generating fonction
The eighth axes
· Chebyshev’s
· Law of large numbers
The nineth axes
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After studying STATISTICS 2, the student will be able to understand:- The concept of probability and its distribution methods.- Discrete and continuous random variables.- Probability distributions, both discrete and continuous. -
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