Suppose you reach into your pocket and pull out a coin; think of one side as “heads” and the other as “tails.” You toss the coin three times. We could now define some random variables, at least informally, e.g., • the number of heads on the first toss (which is 0 or 1), • the total number of heads (which is 0, 1, 2, or 3). This experiment is a little hypothetical—hence the subjunctive voice. If...

Many current local search algorithms for SAT fall into one of two classes. Random walk algorithms such as Walksat/SKC, Novelty+ and HWSAT are very successful but can be trapped for long periods in deep local minima. Clause weighting algorithms such as DLM, GLS, ESG and SAPS are good at escaping local minima but require expensive smoothing phases in which all weights are updated. We show that Wa...

Let us consider a probability space, a random variable on it and the induced probability space. Now, let us consider a new random variable defined on this new space, and the new probability space induced by it. In this paper, we generalize this composition of randon variables to the case when the first variable is a fuzzy random variable instead of an ordinary random variable.

Continuous random variables are widely used to mathematically describe random phenomenon in engineering and physical sciences. In this paper, we present a higherorder logic formalization of the Standard Uniform random variable as the limit value of the sequence of its discrete approximations. We then show the correctness of this specification by proving the corresponding probability distributio...

Repairable system analysis is in nature an evaluation of repair effects. Recent tendency in reliability engineering literature was imposing repair regimes and estimate system repair effects or linking repair to certain covariate to extract repair impacts. Hinted by engineering tune up exercises, we propose a repair model in terms of random variable distribution with a fuzzy parameter because fu...

Random Forests are commonly applied for data prediction and interpretation. The latter purpose is supported by variable importance measures that rate the relevance of predictors. Yet existing measures can not be computed when data contains missing values. Possible solutions are given by imputation methods, complete case analysis and a newly suggested importance measure. However, it is unknown t...

Contents 1. Introduction. 2. The distribution function of a random variable. 3. Classification of random variables. 4. Some special discrete probability distributions. 5. Some special continuous probability distributions. 6. Location characteristics of a real-valued random variable. 7. Dispersion characteristics of a real-valued random variable. 8. Joint distribution functions. 9. Independence ...

The stability of variable stepsize LMS (VSLMS) algorithms with uncorrelated stationary Gaussian data is studied. It is found that when the stepsize is determined by the past data, the boundedness of the stepsize by the usual stability condition of xed stepsize LMS is su cient for the stability of VSLMS. When the stepsize is also related to the current data, the above constraint is no longer su ...

It is known that if a predictable nondecreasing process generates a bounded potential, then its final value satisfies the Garsia inequality. We prove the converse, that is, a random variable satisfying the Garsia inequality generates a bounded potential. We also propose some useful relations between the Garsia inequality and the Cramer conditions, and different ways how to construct a potential.

-In this paper, the k-μ random variable will be considered and closed form expressions for probability density function (PDF), cumulative distribution function (CDF) and moments for this distribution will be derived. Also, product, ratio, maximum and minimum of two k-μ random variables will be studied and PDFs of these functions calculated in the closed forms. Then, obtained statistical functio...