Probability density function and Standard deviation

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Difference between Probability density function and Standard deviation

Probability density function vs. Standard deviation

In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample. In statistics, the standard deviation is a measure of the amount of variation of a random variable expected about its mean.

Cauchy distribution

The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution.

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Cumulative distribution function

In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by a right-continuous monotone increasing function (a càdlàg function) F \colon \mathbb R \rightarrow satisfying \lim_F(x).

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Expected value

In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.

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Integral

In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations.

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Kurtosis

In probability theory and statistics, kurtosis (from κυρτός, kyrtos or kurtos, meaning "curved, arching") is a measure of the "tailedness" of the probability distribution of a real-valued random variable.

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Mean

A mean is a numeric quantity representing the center of a collection of numbers and is intermediate to the extreme values of a set of numbers.

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Normal distribution

In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.

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Normalizing constant

In probability theory, a normalizing constant or normalizing factor is used to reduce any probability function to a probability density function with total probability of one.

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Probability distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment.

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Random variable

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events.

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Variance

In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable.

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