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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. Expected value - Wikipedia

    en.wikipedia.org/wiki/Expected_value

    The second fundamental observation is that any random variable can be written as the difference of two nonnegative random variables. Given a random variable X, one defines the positive and negative parts by X + = max(X, 0) and X − = −min(X, 0). These are nonnegative random variables, and it can be directly checked that X = X + − X −.

  4. Probability density function - Wikipedia

    en.wikipedia.org/wiki/Probability_density_function

    This is also called a "change of variable" and is in practice used to generate a random variable of arbitrary shape f g(X) = f Y using a known (for instance, uniform) random number generator. It is tempting to think that in order to find the expected value E(g(X)), one must first find the probability density f g(X) of the new random variable Y ...

  5. Algebra of random variables - Wikipedia

    en.wikipedia.org/wiki/Algebra_of_random_variables

    Random variables are assumed to have the following properties: complex constants are possible realizations of a random variable; the sum of two random variables is a random variable; the product of two random variables is a random variable; addition and multiplication of random variables are both commutative; and

  6. Probability distribution - Wikipedia

    en.wikipedia.org/wiki/Probability_distribution

    A real-valued discrete random variable can equivalently be defined as a random variable whose cumulative distribution function increases only by jump discontinuities—that is, its cdf increases only where it "jumps" to a higher value, and is constant in intervals without jumps. The points where jumps occur are precisely the values which the ...

  7. Conditional expectation - Wikipedia

    en.wikipedia.org/wiki/Conditional_expectation

    If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a subset of those values. More formally, in the case when the random variable is defined over a discrete probability space, the "conditions" are a partition of this probability space.

  8. Variance - Wikipedia

    en.wikipedia.org/wiki/Variance

    Being a function of random variables, the sample variance is itself a random variable, and it is natural to study its distribution. In the case that Y i are independent observations from a normal distribution , Cochran's theorem shows that the unbiased sample variance S 2 follows a scaled chi-squared distribution (see also: asymptotic ...

  9. Likelihood function - Wikipedia

    en.wikipedia.org/wiki/Likelihood_function

    Let be a discrete random variable with probability mass function depending on a parameter .Then the function = = (=),considered as a function of , is the likelihood function, given the outcome of the random variable .