Roughly speaking, continuous random variables
are found in studies with morphometry, whereas discrete random variables are more common in stereological studies (because they are based on the counts of points and intercepts).
KEYWORDS: continuous random variables
, computer simulations, Monte Carlo methods, MATLAB.
They cover sets, measure, and probability; elementary probability; discrete random variables; continuous random variables
; limit theorems; and random walks.
Let [X.sub.1], ..., [X.sub.T] be T continuous random variables
with a density function f([x.sub.1], ..., [x.sub.T]), where f([x.sub.1], ..., [x.sub.T]) > 0 for ([x.sub.1], ..., [x.sub.T]) [member of] [D.sup.T] and [D.sup.T] is defined in a similar way to [D.sup.3].
In this paper, we consider network flow systems in which the functional capacities of the arcs are continuous random variables
. The investigated problem is to expand the nominal capacities of arcs so that the system would be capable of securing the demands, while the expansion cost is minimal.
Among their topics are initial considerations for reliability design, discrete and continuous random variables
, modeling and reliability basics, the Markov analysis of repairable and non-repairable systems, Six Sigma tools for predictive engineering, a case study of updating reliability estimates, and complex high availability system analysis.
Chapters cover both conceptual and theoretical understanding of discrete and continuous random variables
, hypothesis testing, simple regression, nonparametric statistics, and more.
They and their contributors cover Ostrowski-type results in certain distribution functions, other Ostrowski-type results and applications for probability density functions (PDFs) trapezoidal type results and applications for PDFs, inequalities for cumulative distribution functions via Gruss-type results, elementary inequalities for variants, inequalities for n-type time differential PDFs including Lebesque norms, and variances and moments of continuous random variables
defined over a finite period.
Rounding of continuous random variables
and oscillatory asymptotics.