A probabilistic system is one where events and occurrences cannot be predicted with precise accuracy. It is contrasted by a deterministic system in which all events can be predicted with certainty.Know More
In a probabilistic system, unlike in a deterministic system, what has just occurred is not always an accurate predictor of what will transpire next. The weather, for example, is a probabilistic system, in that future events can only be imperfectly predicted.
The theory of probabilistic systems by extension leads to probabilistic analysis and forecasting. A probabilistic system must be analyzed according to the various possible outcomes and their relative probability of occurrence.Learn more about Statistics
The theoretical definition of probability states that if the outcomes of an event are mutually exclusive and equally likely to happen, then the probability of the outcome "A" is: P(A) = Number of outcomes that favors A / Total number of outcomes. For example, there are two possible outcomes when a coin is tossed in the air, and the probability of the coin landing on a head or a tail is equal to 0.5.Full Answer >
Standard deviation is a measure of the variation or diversity of scores in a set of data. It is used to determine how much data varies from the average of a population. The larger the deviation, the more spread out the data set. Standard deviation is represented by the Greek letter sigma.Full Answer >
To find the derivative of a given function, plug the function into the derivative formula, distribute all of the terms, and then cancel all possible terms to eliminate the formula's denominator. Once the formula is simplified, set h to approach zero to find the derivative.Full Answer >
Chebyshev's theorem, or inequality, states that for any given data sample, the proportion of observations is at least (1-(1/k2)), where k equals the "within number" divided by the standard deviation. For this to work, k must equal at least 1. This theorem provides a way to know what percentage of data lies within the standard deviations from any data set.Full Answer >