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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).
For example, the conditional probability that someone unwell (sick) is coughing might be 75%, in which case we would have that P(Cough) = 5% and P(Cough|Sick) = 75 %. Although there is a relationship between A and B in this example, such a relationship or dependence between A and B is not necessary, nor do they have to occur simultaneously.
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 .
In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. 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 ...
Condition numbers can also be defined for nonlinear functions, and can be computed using calculus.The condition number varies with the point; in some cases one can use the maximum (or supremum) condition number over the domain of the function or domain of the question as an overall condition number, while in other cases the condition number at a particular point is of more interest.
Taking the expectation of this conditional variance across all values of X gives [ ()], often termed the “unexplained” or within-group part. The variance of the conditional mean, Var ( E [ Y ∣ X ] ) {\displaystyle \operatorname {Var} (\operatorname {E} [Y\mid X])} , measures how much these conditional means differ (i.e. the ...
For example, suppose P(L = red) = 0.2, P(L = yellow) = 0.1, and P(L = green) = 0.7. Multiplying each column in the conditional distribution by the probability of that column occurring results in the joint probability distribution of H and L, given in the central 2×3 block of entries. (Note that the cells in this 2×3 block add up to 1).
In statistics, a truncated distribution is a conditional distribution that results from restricting the domain of some other probability distribution.Truncated distributions arise in practical statistics in cases where the ability to record, or even to know about, occurrences is limited to values which lie above or below a given threshold or within a specified range.