Search results
Results from the WOW.Com Content Network
By grouping together all of the clauses that use the same variable, and applying the inference rule to each pair of clauses, it is possible to find all inferences that are possible from a given 2-CNF instance, and to test whether it is consistent, in total time O(n 3), where n is the number of variables in the instance. This formula comes from ...
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.
Given two events A and B from the sigma-field of a probability space, with the unconditional probability of B being greater than zero (i.e., P(B) > 0), the conditional probability of A given B (()) is the probability of A occurring if B has or is assumed to have happened. [5]
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.
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 −.
Let T be survival time, which is any positive number. A particular time is designated by the lower case letter t. The cumulative distribution function of T is the function = (), where the right-hand side represents the probability that the random variable T is less than or equal to t.
Binomial distribution, for the number of "positive occurrences" (e.g. successes, yes votes, etc.) given a fixed total number of independent occurrences; Negative binomial distribution, for binomial-type observations but where the quantity of interest is the number of failures before a given number of successes occurs
The formulas given in the previous section allow one to calculate the point estimates of α and β — that is, the coefficients of the regression line for the given set of data. However, those formulas do not tell us how precise the estimates are, i.e., how much the estimators ^ and ^ vary from sample to sample for the specified sample size.