DISTRIBUTION FUNCTION Meaning and
Definition
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A distribution function, also referred to as a cumulative distribution function (CDF), is a fundamental concept in probability theory and statistics. It describes the probability of a random variable taking on a value less than or equal to a specific value. In simple terms, it represents the cumulative probability of a random variable.
The distribution function is denoted by F(x) and is defined for all possible values of x in the range of the random variable. It is a non-decreasing function that ranges from 0 to 1. For every value of x, F(x) gives the probability of the random variable being less than or equal to x.
The distribution function characterizes the probability distribution of a random variable and provides essential information about its behavior. By evaluating the distribution function, one can determine various statistical properties such as the median, expected value, quartiles, and percentiles of a random variable.
A well-known example of a distribution function is the cumulative distribution function of the normal distribution, known as the standard normal distribution function or the z-score chart. This distribution function allows one to comprehend the likelihood of obtaining values within a specific range for a normally distributed random variable.
Overall, the distribution function serves as a valuable tool for analyzing and understanding the probabilities associated with random variables in probability theory and statistics.
Common Misspellings for DISTRIBUTION FUNCTION
- sistribution function
- xistribution function
- cistribution function
- fistribution function
- ristribution function
- eistribution function
- dustribution function
- djstribution function
- dkstribution function
- dostribution function
- d9stribution function
- d8stribution function
- diatribution function
- diztribution function
- dixtribution function
- didtribution function
- dietribution function
- diwtribution function
- disrribution function
- disfribution function
Etymology of DISTRIBUTION FUNCTION
The word "distribution" in the context of probability theory and statistics originates from the Latin word "distributio", which means "a dividing" or "an apportioning". It comes from the verb "distribuere", which is formed by combining "dis-" (meaning "apart" or "in different directions") and "tribuere" (meaning "to assign" or "to allot").
The term "distribution function" specifically refers to the cumulative distribution function (CDF), which describes the probability distribution of a random variable. The CDF gives the probability that a random variable takes on a value less than or equal to a given point. The usage of "distribution function" in this context can be traced back to the early 20th century development of probability theory and statistics.
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