Lecture
where n x is the number of sample values less than x ; n is the sample size.
(unbiased, consistent estimate of the expectation)
where x i - sample values; n is the sample size.
(biased, consistent estimate of variance)
(unbiased, consistent estimate of variance)
distribution of random variable X In the discrete case
Where 
- sample values.
In absolutely continuous case
Where 
- distribution density X.
1. For a mathematical expectation with a known variance 
where t p is the root of the equation 
; 
- Laplace function.
2. For mathematical expectation with unknown variance
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
Where 
, 
are from the conditions:
- random variable distributed by law 
with n - 1 degrees of freedom.
Selective correlation moment of X and Y values
- sample averages X and Y, respectively.
Selective correlation coefficient
Where 
- selective dispersions of X and Y values.
Selective regression coefficient Y to X
Selective regression equation
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Probability theory. Mathematical Statistics and Stochastic Analysis
Terms: Probability theory. Mathematical Statistics and Stochastic Analysis