You get a bonus - 1 coin for daily activity. Now you have 1 coin

Mathematical statistics

Lecture



Empirical distribution function

  Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics

where n x is the number of sample values ​​less than x ; n is the sample size.


Selective average

(unbiased, consistent estimate of the expectation)


  Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics

where x i - sample values; n is the sample size.


Selective dispersion

(biased, consistent estimate of variance)


  Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics


Corrected sample variance

(unbiased, consistent estimate of variance)


  Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics

Likelihood function for estimating unknown parameter   Mathematical statistics   Mathematical statistics distribution of random variable X

In the discrete case

  Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics

Where   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics - sample values.

In absolutely continuous case

  Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics

Where   Mathematical statistics   Mathematical statistics - distribution density X.


Confidence intervals with a confidence factor p in the case of a normally distributed population

1. For a mathematical expectation with a known variance   Mathematical statistics   Mathematical statistics

  Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics

where t p is the root of the equation   Mathematical statistics   Mathematical statistics   Mathematical statistics ;   Mathematical statistics   Mathematical statistics - Laplace function.

2. For mathematical expectation with unknown variance

  Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics

s 2 is the sample variance; t p satisfies the condition P (| t n-1 | < t p ) = p ; t n-1 is a random variable distributed according to Student’s law with n - 1 degrees of freedom.

3. For dispersion

  Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics

Where   Mathematical statistics   Mathematical statistics ,   Mathematical statistics   Mathematical statistics are from the conditions:

  Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics

  Mathematical statistics   Mathematical statistics - random variable distributed by law   Mathematical statistics   Mathematical statistics with n - 1 degrees of freedom.

Selective correlation moment of X and Y values

  Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics

  Mathematical statistics   Mathematical statistics   Mathematical statistics - sample averages X and Y, respectively.


Selective correlation coefficient

  Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics

Where   Mathematical statistics   Mathematical statistics   Mathematical statistics - selective dispersions of X and Y values.


Selective regression coefficient Y to X

  Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics


Selective regression equation

  Mathematical statistics   Mathematical statistics   Mathematical statistics   Mathematical statistics


Comments


To leave a comment
If you have any suggestion, idea, thanks or comment, feel free to write. We really value feedback and are glad to hear your opinion.
To reply

Probability theory. Mathematical Statistics and Stochastic Analysis

Terms: Probability theory. Mathematical Statistics and Stochastic Analysis