Sentence examples for analytical probability from inspiring English sources

Approximations by analytical probability density functions using dimensionless variables are proposed.

which is an important tool in analytical probability theory, statistical physics and physical chemistry.

Tsarouhas (2015) developed analytical probability models for an automated serial production, which consists of n-machines in series.

It is verified that the analytical probability distribution model is a reasonable model to estimate the peak pressure coefficients.

Analytical probability models for an automated system that consists of n-machines in series with common transfer mechanism and control system are developed.

Moreover, these figures show a validation of the joint distribution given in Theorem 1. Fig. 2 Empirical and analytical probability density functions of the SCN of the central semi-correlated Wishart matrices as N varies Fig. 3 Empirical and analytical probability density function of the SCN of the central semi-correlated Wishart matrices as ρ varies.

Hence, we have developed a simple numerical procedure, based on analytical probabilities, suitable for instrumental design and evaluation.

It follows that the expression of the semi-analytical probability density function is expressed as begin{array}rcl@ widetilde{f}(x;h) &=& frac{1}{Nh} sumlimits_{i=1}^{N} vleft(frac{x-x_{i}}{h}right).

To measure the semi-analytical probability density of the received sample, we have considered a digital modulation scheme which uses bit-phase-shift keying (BPSK) for bit-to-symbol conversion.

Figure 4 compares the derived analytical transmission probability with the analytical transmission probability which does not consider the retry limit.

Fig. 4 Analytical marking probability.