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  2. Random variable - Wikipedia

    en.wikipedia.org/wiki/Random_variable

    A mixed random variable is a random variable whose cumulative distribution function is neither discrete nor everywhere-continuous. [10] It can be realized as a mixture of a discrete random variable and a continuous random variable; in which case the CDF will be the weighted average of the CDFs of the component variables. [10]

  3. Continuous or discrete variable - Wikipedia

    en.wikipedia.org/.../Continuous_or_discrete_variable

    In probability theory and statistics, the probability distribution of a mixed random variable consists of both discrete and continuous components. A mixed random variable does not have a cumulative distribution function that is discrete or everywhere-continuous. An example of a mixed type random variable is the probability of wait time in a queue.

  4. Probability theory - Wikipedia

    en.wikipedia.org/wiki/Probability_theory

    Probability theory or probability calculus is the branch of mathematics concerned with probability.Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms.

  5. Expected value - Wikipedia

    en.wikipedia.org/wiki/Expected_value

    According to the change-of-variables formula for Lebesgue integration, [21] combined with the law of the unconscious statistician, [22] it follows that ⁡ [] = for any absolutely continuous random variable X. The above discussion of continuous random variables is thus a special case of the general Lebesgue theory, due to the fact that every ...

  6. Mean - Wikipedia

    en.wikipedia.org/wiki/Mean

    If the random variable is denoted by , then the mean is also known as the expected value of (denoted ()). For a discrete probability distribution , the mean is given by ∑ x P ( x ) {\displaystyle \textstyle \sum xP(x)} , where the sum is taken over all possible values of the random variable and P ( x ) {\displaystyle P(x)} is the probability ...

  7. Weibull distribution - Wikipedia

    en.wikipedia.org/wiki/Weibull_distribution

    In probability theory and statistics, the Weibull distribution / ˈ w aɪ b ʊ l / is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page.

  8. Normal distribution - Wikipedia

    en.wikipedia.org/wiki/Normal_distribution

    A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.

  9. Probability density function - Wikipedia

    en.wikipedia.org/wiki/Probability_density_function

    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 ...