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If the conditional distribution of given is a continuous distribution, then its probability density function is known as the conditional density function. [1] The properties of a conditional distribution, such as the moments , are often referred to by corresponding names such as the conditional mean and conditional variance .
This distribution is also known as the conditional Poisson distribution [1] or the positive Poisson distribution. [2] It is the conditional probability distribution of a Poisson-distributed random variable, given that the value of the random variable is not zero. Thus it is impossible for a ZTP random variable to be zero. Consider for example ...
In statistics, the conditional probability table (CPT) is defined for a set of discrete and mutually dependent random variables to display conditional probabilities of a single variable with respect to the others (i.e., the probability of each possible value of one variable if we know the values taken on by the other variables).
The Birnbaum–Saunders distribution, also known as the fatigue life distribution, is a probability distribution used extensively in reliability applications to model failure times. The chi distribution. The noncentral chi distribution; The chi-squared distribution, which is the sum of the squares of n independent Gaussian random variables.
The resulting limit is the conditional probability distribution of Y given X and exists when the denominator, the probability density (), is strictly positive. It is tempting to define the undefined probability P ( A ∣ X = x ) {\displaystyle P(A\mid X=x)} using limit ( 1 ), but this cannot be done in a consistent manner.
The value x = 0.5 is an atom of the distribution of X, thus, the corresponding conditional distribution is well-defined and may be calculated by elementary means (the denominator does not vanish); the conditional distribution of Y given X = 0.5 is uniform on (2/3, 1). Measure theory leads to the same result.
In probability theory, the chain rule [1] (also called the general product rule [2] [3]) describes how to calculate the probability of the intersection of, not necessarily independent, events or the joint distribution of random variables respectively, using conditional probabilities.
In probability theory, regular conditional probability is a concept that formalizes the notion of conditioning on the outcome of a random variable. The resulting conditional probability distribution is a parametrized family of probability measures called a Markov kernel .