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For events in B, two conditions must be met: the probability of B is one and the relative magnitudes of the probabilities must be preserved. The former is required by the axioms of probability , and the latter stems from the fact that the new probability measure has to be the analog of P in which the probability of B is one - and every event ...
In essence probability is influenced by a person's information about the possible occurrence of an event. For example, let the event A {\displaystyle A} be 'I have a new phone'; event B {\displaystyle B} be 'I have a new watch'; and event C {\displaystyle C} be 'I am happy'; and suppose that having either a new phone or a new watch increases ...
More generally, one can refer to the conditional distribution of a subset of a set of more than two variables; this conditional distribution is contingent on the values of all the remaining variables, and if more than one variable is included in the subset then this conditional distribution is the conditional joint distribution of the included ...
Conditional independence depends on the nature of the third event. If you roll two dice, one may assume that the two dice behave independently of each other. Looking at the results of one die will not tell you about the result of the second die. (That is, the two dice are independent.)
Wilner, Walkley, & Cook, two years prior to The Nature of Prejudice, studied segregation and integration in housing projects, and also suggested four conditions under which intergroup attitudes would change for the better.
Any conditional statement consists of at least one sufficient condition and at least one necessary condition. In data analytics , necessity and sufficiency can refer to different causal logics, [ 7 ] where necessary condition analysis and qualitative comparative analysis can be used as analytical techniques for examining necessity and ...
Thus if n is a large even integer and m is a number between 3 and n / 2 , then one might expect the probability of m and n − m simultaneously being prime to be 1 / ln m ln(n − m) . If one pursues this heuristic, one might expect the total number of ways to write a large even integer n as the sum of two odd primes to be roughly
Assume that the combined system determined by two random variables and has joint entropy (,), that is, we need (,) bits of information on average to describe its exact state. Now if we first learn the value of X {\displaystyle X} , we have gained H ( X ) {\displaystyle \mathrm {H} (X)} bits of information.