A Gaussian function, also known as a normal distribution or bell curve, is a function that describes how the values of a variable are distributed symmetrically around the mean, with most values clustering around the central peak and probabilities tapering off towards the tails. It is fundamental in statistics and probability theory due to the Central Limit Theorem, which states that the sum of many independent random variables tends toward a Gaussian distribution, regardless of the original distribution of the variables.

Gaussian Function

Gaussian function

The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution characterized by its symmetrical bell-shaped curve, where the mean, median, and mode are all equal. It is fundamental in statistics because many natural phenomena and measurement errors are approximately normally distributed, making it a cornerstone for statistical inference and hypothesis testing.

normal distribution

The bell curve, also known as the normal distribution, is a statistical concept that describes how data points are distributed around a mean in a symmetrical, bell-shaped curve. It is fundamental in statistics because many phenomena naturally follow this distribution, allowing for predictions and inferences about populations from sample data.

bell curve

values of a variable

distributed symmetrically around the mean

clustering around the central peak

probabilities tapering off towards the tails

fundamental in statistics

Probability theory is a branch of mathematics that deals with the analysis and interpretation of random phenomena and the likelihood of various outcomes. It provides a framework for quantifying uncertainty and making predictions based on incomplete information, which is fundamental in fields ranging from statistics to quantum mechanics.

probability theory

The Central Limit Theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size becomes larger, regardless of the population's original distribution. This theorem is foundational in statistics because it allows for the application of inferential techniques to make predictions and decisions based on sample data.

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