In classical Bernoulli processes, it is assumed that a single Bernoulli experiment can be described by a precise and precisely known probability distribution. However, both of these assumptions can be relaxed. A first approach, often used in sensitivity analysis, is to drop only the second assumption: one assumes the existence of a precise distribution, but has insufficient resources to determi...

Consider a nite alphabet with a probability distribution p. We study the probability (p) of obtaining a palindrome in a nite time by independent draws. Using a Mahler equation for an associated generating function, we give a closed form expression for (p). Moreover we describe completely the cases where (p) has value less than 1, in connection with the singularities of the generating function. ...

Specialised literature presents a number of models describing the function of the vocal folds. In most of those models an emphasis is placed on the effect of Bernoulli’s air underpressure during the air passage through the glottis. The author defines a principle of the vocal folds function with a working version name „principle of the compressed air bubble“. The paper deals with the experimenta...

Based upon previous studies on laws of large numbers for fuzzy, random, fuzzy random and random fuzzy variables, We go further to explore weak law of large numbers(WLLN) for hybrid variables comprising fuzzy random variables and random fuzzy variables. we mainly prove Chebyshev WLLN, Poisson WLLN, Bernoulli WLLN, Markov WLLN and Khintchin WLLN for hybrid variables based on chance measure.

In this note we show how the properties of association and negative association can be combined with Stein’s method for compound Poisson approximation. Applications include k–runs in iid Bernoulli trials, an urn model with urns of limited capacity and extremes of random variables.

Abstract: For each n ≥ 1, let {Xn,j , j ≥ 1} be i.i.d. Bernoulli random variables with P{Xn,1 = 1} = pn = 1 − qn = 1 − P{Xn,1 = 0}, 0 < pn < 1. Define Wn,mn = ∑mn j=1 (Rn,j −an), where Rn,j = inf{k ≥ 0 : Xn,j+k = 0} is the number of success runs starting at j, mn is a sequences of positive integers, and an = pn/qn. We show that, under the condition mnpn → ∞, the central limit theorem Wn,mn σmn ...

The static pull-in instability of beam-type micro-electromechanical systems is theoretically investigated. Two engineering cases including cantilever and double cantilever micro-beam are considered. Considering the mid-plane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, c...

In this paper, the stability of a functionally graded magneto-electro-elastic (FG-MEE) micro-beam under actuation of electrostatic pressure is studied. For this purpose Euler-Bernoulli beam theory and constitutive relations for magneto-electro-elastic (MEE) materials have been used. We have supposed that material properties vary exponentially along the thickness direction of the micro-beam. Gov...