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Interactive MATLAB‐based demo program for sum of independent random variables [PDF]

Computer Applications in Engineering Education, 2013
We present an interactive MATLAB-based demo program devoted to teaching undergraduate students the behavior of the sum of independent random variables. The user chooses the type of the variables, and the parameters of these variables. The sum is shown in
GORDANA Jovanović Dolecek
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On the Lower Limit of Sums of Independent Random Variables

The Annals of Mathematics, 1947
Als Gegenstück der von W. Feller neulich erreichten vollständigen Klärung des Satzes von iterierten Logarithmus, d. h. vom oberen Grenzwert der Summe \(S_n=\sum_{\nu=1}^n X_\nu\) unabhängiger Zufallsveränderlichen \(X_\nu\) für \(n \to \infty\), wird folgender Satz bewiesen: Im Falle einer Alternative mit Pr\((X_\nu =1)=p\) und \(\text{Pr }(X_\nu=0 ...
Chung, Kai Lai, Erdős, Pál
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The Behavior of Sums of Independent Random Variables

Theory of Probability & Its Applications, 1975
werden ausgedehnt auf die Situation: \(\vert a_n^{-1}(S_n - \text{Med}(S_n))\vert\) bleibt mit \(P=1\) beschränkt \((a_n\to\infty\) geeignet), die als äquivalent zu \[ a_n^{-1} b_n^{-1} (S_n - \text{Med}(S_n)) \text{ konvergiert gegen Null mit }P=1 \] nachgewiesen wird \((b_n\to\infty\) geeignet).
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Sums of independent fuzzy random variables

Fuzzy Sets and Systems, 2001
The paper deals with almost-sure-convergence of sums of independent fuzzy random variables. Via support functions, the fuzzy number space can be embedded as a cone into a Banach space and convergence results of Banach-space-valued random variables can be used (similarly to earlier papers by Klement/Puri/Ralescu and Körner). The author especially proves
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FLUCTUATIONS OF SUMS OF INDEPENDENT RANDOM VARIABLES

The Annals of Mathematics, 1950
1. One aspect of the theory of addition of independent random variables is the frequency with which the partial sums change sign. Investigations of this nature were originated by Paul L6vy, in a paper [1] which contains a wealth of ideas. This problem as such was mentioned by Feller in his 1945 address [2].
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Note on “sums of independent fuzzy random variables”

Fuzzy Sets and Systems, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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