Probability distributionIn probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.
Probability theoryProbability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space.
Variable starA variable star is a star whose brightness as seen from Earth (its apparent magnitude) changes with time. This variation may be caused by a change in emitted light or by something partly blocking the light, so variable stars are classified as either: Intrinsic variables, whose luminosity actually changes; for example, because the star periodically swells and shrinks. Extrinsic variables, whose apparent changes in brightness are due to changes in the amount of their light that can reach Earth; for example, because the star has an orbiting companion that sometimes eclipses it.
ProbabilityProbability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin.
Sun-4Sun-4 is a series of Unix workstations and servers produced by Sun Microsystems, launched in 1987. The original Sun-4 series were VMEbus-based systems similar to the earlier Sun-3 series, but employing microprocessors based on Sun's own SPARC V7 RISC architecture in place of the 68k family processors of previous Sun models. Sun 4/280 was known as base system that was used for building of first RAID prototype. Models are listed in approximately chronological order. {| class="wikitable sortable" |- !Model !Codename !CPU board !CPU !CPU MHz !Max.
Sun-3Sun-3 is a series of UNIX computer workstations and servers produced by Sun Microsystems, launched on September 9, 1985. The Sun-3 series are VMEbus-based systems similar to some of the earlier Sun-2 series, but using the Motorola 68020 microprocessor, in combination with the Motorola 68881 floating-point co-processor (optional on the Sun 3/50) and a proprietary Sun MMU. Sun-3 systems were supported in SunOS versions 3.0 to 4.1.1_U1 and also have current support in NetBSD and Linux.
Sun-2The Sun-2 series of UNIX workstations and servers was launched by Sun Microsystems in November 1983. As the name suggests, the Sun-2 represented the second generation of Sun systems, superseding the original Sun-1 series. The Sun-2 series used a 10 MHz Motorola 68010 microprocessor with a proprietary Sun-2 Memory Management Unit (MMU), which enabled it to be the first Sun architecture to run a full virtual memory UNIX implementation, SunOS 1.0, based on 4.1BSD.
SinIn a religious context, 'sin' is a transgression against divine law or a law of God. Each culture has its own interpretation of what it means to commit a sin. While sins are generally considered actions, any thought, word, or act considered immoral, selfish, shameful, harmful, or alienating might be termed "sinful".
Semiregular variable starIn astronomy, a semiregular variable star, a type of variable star, is a giant or supergiant of intermediate and late (cooler) spectral type showing considerable periodicity in its light changes, accompanied or sometimes interrupted by various irregularities. Periods lie in the range from 20 to more than 2000 days, while the shapes of the light curves may be rather different and variable with each cycle. The amplitudes may be from several hundredths to several magnitudes (usually 1-2 magnitudes in the V filter).
Sun-1Sun-1 was the first generation of UNIX computer workstations and servers produced by Sun Microsystems, launched in May 1982. These were based on a CPU board designed by Andy Bechtolsheim while he was a graduate student at Stanford University and funded by DARPA. The Sun-1 systems ran SunOS 0.9, a port of UniSoft's UniPlus V7 port of Seventh Edition UNIX to the Motorola 68000 microprocessor, with no window system. Affixed to the case of early Sun-1 workstations and servers is a red bas relief emblem with the word SUN spelled using only symbols shaped like the letter U.
Dependent and independent variablesDependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function), on the values of other variables. Independent variables, in turn, are not seen as depending on any other variable in the scope of the experiment in question. In this sense, some common independent variables are time, space, density, mass, fluid flow rate, and previous values of some observed value of interest (e.
Joint probability distributionGiven two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs. The joint distribution can just as well be considered for any given number of random variables. The joint distribution encodes the marginal distributions, i.e. the distributions of each of the individual random variables. It also encodes the conditional probability distributions, which deal with how the outputs of one random variable are distributed when given information on the outputs of the other random variable(s).
Conditional probabilityIn probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(AB) or occasionally P_B(A).
Mortal sinA mortal sin (peccatum mortale), in Catholic theology, is a gravely sinful act which can lead to damnation if a person does not repent of the sin before death. It is alternatively called deadly, grave, and serious. A sin is considered to be "mortal" when its quality is such that it leads to a separation of that person from God's saving grace. Three conditions must together be met for a sin to be mortal: "Mortal sin is sin whose object is grave matter and which is also committed with full knowledge and deliberate consent.
Probability axiomsThe Kolmogorov axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases. An alternative approach to formalising probability, favoured by some Bayesians, is given by Cox's theorem. The assumptions as to setting up the axioms can be summarised as follows: Let be a measure space with being the probability of some event , and .
Probability spaceIn probability theory, a probability space or a probability triple is a mathematical construct that provides a formal model of a random process or "experiment". For example, one can define a probability space which models the throwing of a die. A probability space consists of three elements: A sample space, , which is the set of all possible outcomes. An event space, which is a set of events, , an event being a set of outcomes in the sample space. A probability function, , which assigns each event in the event space a probability, which is a number between 0 and 1.
Christian views on sinIn Christianity, 'sin' is an immoral act considered to be a transgression of divine law. The doctrine of sin is central to the Christian faith, since its basic message is about redemption in Christ. Hamartiology, a branch of Christian theology which is the study of sin, describes sin as an act of offence against God by despising his persons and Christian biblical law, and by injuring others. Christian hamartiology is closely related to concepts of natural law, moral theology and Christian ethics.
Sun MicrosystemsSun Microsystems, Inc. (Sun for short), was an American technology company that sold computers, computer components, software, and information technology services and created the Java programming language, the Solaris operating system, ZFS, the (NFS), and SPARC microprocessors. Sun contributed significantly to the evolution of several key computing technologies, among them Unix, RISC processors, thin client computing, and virtualized computing. Notable Sun acquisitions include Cray Business Systems Division, Storagetek, and Innotek GmbH, creators of VirtualBox.
Eternal sinIn Christian hamartiology, eternal sin, the unforgivable sin, unpardonable sin, or ultimate sin is the sin which will not be forgiven by God. One eternal or unforgivable sin (blasphemy against the Holy Spirit), also known as the sin unto death, is specified in several passages of the Synoptic Gospels, including Mark 3:28–29, Matthew 12:31–32, and Luke 12:10, as well as other New Testament passages including Hebrews 6:4–6, Hebrews 10:26–31, and 1 John 5:16.
Bayesian probabilityBayesian probability (ˈbeɪziən or ˈbeɪʒən ) is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief. The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses; that is, with propositions whose truth or falsity is unknown.
