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Journal of Mathematics and Applications
2009 Vol. 31 51-66
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Demonstratio Mathematica
 EN Let: {Xi} be a sequence of r.v.'s, and: Mn := max (X1,..., Xn), mn := min (X1,..., Xn). Our goal is to prove the almost sure central limit theorem for the properly normalized vector {Mn,mn}, provided: 1) {Xi} is an i.i.d. sequence, 2) {Xi} is a certain standardized stationary Gaussian sequence.
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84%
Bulletin of the Polish Academy of Sciences. Mathematics
 EN We prove that the hyperbolic Hausdorff dimension of Fr Ω, the boundary of the simply connected immediate basin of attraction Ω to an attracting periodic point of a rational mapping of the Riemann sphere, which is not a finite Blaschke product in some holomorphic coordinates, or a 2 : 1 factor of a B[...]
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Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
2014 Vol. 19 51--55
 EN The Central Limit Theorem states that regardless of the underlying distribution, the distribution of the sample means approaches normality as the sample size increases. This paper describes the steps in MS Excel to help students’ better understanding of this theorem.
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Demonstratio Mathematica
 EN In our paper we prove two kinds of the so-called almost sure central limit theorem (ASCLT). The first one is the ASCLT for the vectors ((Mn(1) , . . . ,Mn(r)), where Mn(j) n - the j-th largest maximum of X1, . . . ,Xn and {Xi} is an i.i.d. sequence. Our second result is the ASCLT for some random per[...]
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