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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.
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 .
The formula counting all functions N → X is not useful here, because the number of them grouped together by permutations of N varies from one function to another. Rather, as explained under combinations , the number of n -multicombinations from a set with x elements can be seen to be the same as the number of n -combinations from a set with x ...
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 ...
For a value x in V and an event A, the conditional probability is given by (=). Writing (,) = (=) for short, we see that it is a function of two variables, x and A. For a fixed A, we can form the random variable = (,).
Probability density function (pdf) or probability density: 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 equal that sample.
An 11-year-old girl who was taken to a hospital in critical condition after attempting to save her 12-year-old classmate's life when he fell through the surface of an icy upstate New York lake has ...
Throughout, will be a topological space. The definition of meagre set uses the notion of a nowhere dense subset of , that is, a subset of whose closure has empty interior.See the corresponding article for more details.