Probability of events

To ensure that the probability of events giving rise to significant exposures and the magnitude of such exposures are kept as low as reasonably achievable, economic and social factors being taken into account. 

The mathematical properties of P(A), tlie probability of event A, are deduced from tlie following postulates governing tlie assigmiient of probabilities to tlie elements of a sample space, S. 

The conditional probability of event B given A is denoted by P(B A) and defined as... 

Tlie matliematical properties of P(A), tlie probability of event A, are deduced from tlie following postulates governing tlie assignment of probabilities to tlie elements of a sample space, S. In the case of a discrete sample space (i.e., a sample space consisting of a finite nmnber or countable infinitude of elements), tliese postulates require that the numbers assigned as probabilities to tlie elements of S be nonnegative and have a sum equal to 1. 

Tlie conditional probability of event B, no failures in 10 years, given tliat tlie failure rate is Z per year, is obtained by applying the Poisson distribution to give... 

In mathematics, Laplace s name is most often associated with the Laplace transform, a technique for solving differential equations. Laplace transforms are an often-used mathematical tool of engineers and scientists. In probability theory he invented many techniques for calculating the probabilities of events, and he applied them not only to the usual problems of games but also to problems of civic interest such as population statistics, mortality, and annuities, as well as testimony and verdicts. 

One important consequence of this definition is that if lt - are statistically independent random variables then all groups of events of the form x in Aj, 2 in A2, , n in An are statistically independent.38 This property greatly simplifies the calculation of probabilities of events associated with independent random variables. 

W = probability of event t = probability of presence A = probability of fatal injury Then, one evaluates collective risk R, as... 

Location.Type of Reaction. Quantity, Probability of Event and Propagation... 

Let us introduce the concept of conditional probability. We denote the joint probability of events A and B by p(A,B) and the conditional probability of occurrence of event A given event B by p(A B). Thus, we have... 

The most natural way to introduce aging is through the age-specific failure rate illustrated in the nice book of Cox [94]. To apply Cox s arguments to the BQD physics, we have to identify the failure of a component, for instance an electric light bulb, with the occurrence of an event, as discussed in Section X. According to Cox, let us consider a sequence of the Gibbs ensemble of Section X known not to have produced an event at time t and let r(t) be the limit of the ratio to At of the probability of event occurrence in [t, f+A]. In the usual notation for conditional probability,... 

The probabilities of events were determined with due regard for available statistical data on the analyzed objects. In cases that they were insufficient, the data obtained from other similar objects pertaining to other industry and technology areas were used. 

Hadditional dose commitment by a risk coefficient and a value of individual (collective) dose. The life-long risk coefficient characterizes reduction of the duration offull-valuelifeby 15 years (on average) per one stochastic effect (due to fatal cancers, serious hereditary effects and non-fatal cancers with similar-to-fatal-cancer consequences). 

Intersection probability—The probability of events to occur at the same time. 

Often the probability of an event depends on one or more related events or conditions. Such probabilities are called conditional We will write p A B) for the probability of event A given B (or the probability density of A given B if the sample space of A is continuous). 

To understand why this is so, let us consider briefly systems containing a large number of atoms, typically a number greater than the Avogadro number (ca. 6.02 x 10 ). With such a large number, we may be reasonably sure that the probability of events occurring will be described by Eq. (1). Having said this, however, it is necessary to point out that Eq. (1) applies only to random occurrences, which is to say that all the events under consideration should be random ones and all the entities (particles) involved should exhibit only random behavior. Whether any of the phenomena of nature are strictly random is still a matter of some dispute at the present time. Phenomena may appear to be random only because... 

Odds ratio = probability of event/(l probability of event)... 

Normal Distribution is a continuous probability distribution that is useful in characterizing a large variety of types of data. It is a symmetric, bell-shaped distribution, completely defined by its mean and standard deviation and is commonly used to calculate probabilities of events that tend to occur around a mean value and trail off with decreasing likelihood. Different statistical tests are used and compared the y 2 test, the W Shapiro-Wilks test and the Z-score for asymmetry. If one of the p-values is smaller than 5%, the hypothesis (Ho) (normal distribution of the population of the sample) is rejected. If the p-value is greater than 5% then we prefer to accept the normality of the distribution. The normality of distribution allows us to analyse data through statistical procedures like ANOVA. In the absence of normality it is necessary to use nonparametric tests that compare medians rather than means. 

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