GEOMETRIC DISTRIBUTION Meaning and
Definition
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The geometric distribution is a probability distribution that models the number of independent Bernoulli trials needed to obtain the first success. It is typically used to analyze the probability of success after a series of repeated trials, where each trial has only two outcomes, such as success or failure.
In simple terms, the geometric distribution describes the probability distribution of the number of trials required until the first success occurs. The distribution assumes independent and identical trials, meaning the probability of success remains constant throughout the trials. The probability parameter, often denoted as p, represents the chance of success in each trial.
In the geometric distribution, the random variable represents the number of trials required until the first success occurs. The possible values for this random variable are non-negative integers starting from 1. The distribution is skewed to the right since the number of trials increases as the likelihood of success decreases.
The mean of the geometric distribution is calculated as 1/p, while the variance is given by (1-p)/p^2. These parameters provide insights into the expected average number of trials needed to achieve success and the level of dispersion around this expectation.
The geometric distribution finds applications in various fields, including statistics, probability theory, engineering, and economics. It allows for the analysis of success probabilities, expected outcomes, and the calculation of risk or cost involved in repeated trials until a specific event occurs.
Common Misspellings for GEOMETRIC DISTRIBUTION
- feometric distribution
- veometric distribution
- beometric distribution
- heometric distribution
- yeometric distribution
- teometric distribution
- gwometric distribution
- gsometric distribution
- gdometric distribution
- grometric distribution
- g4ometric distribution
- g3ometric distribution
- geimetric distribution
- gekmetric distribution
- gelmetric distribution
- gepmetric distribution
- ge0metric distribution
- ge9metric distribution
- geonetric distribution
- geoketric distribution
Etymology of GEOMETRIC DISTRIBUTION
The word "geometric" in "geometric distribution" is derived from the Greek word "geōmetrikos", which means "geometrical". The term was first used in mathematics to describe a distribution pattern or sequence that is related to geometric shapes and ratios.
In statistics, the geometric distribution refers to a probability distribution that models the number of trials needed to achieve a success in a sequence of independent Bernoulli trials with the same probability of success. The name "geometric" was given to this distribution because the probabilities associated with different numbers of trials until success can be visualized graphically as areas of geometric shapes, such as triangles or rectangles.
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