Search results
Results from the WOW.Com Content Network
The term law of total probability is sometimes taken to mean the law of alternatives, which is a special case of the law of total probability applying to discrete random variables. [ citation needed ] One author uses the terminology of the "Rule of Average Conditional Probabilities", [ 4 ] while another refers to it as the "continuous law of ...
Also confidence coefficient. A number indicating the probability that the confidence interval (range) captures the true population mean. For example, a confidence interval with a 95% confidence level has a 95% chance of capturing the population mean. Technically, this means that, if the experiment were repeated many times, 95% of the CIs computed at this level would contain the true population ...
The collection of all such events is a sigma-algebra. [3] An event containing exactly one outcome is called an elementary event. The event that contains all possible outcomes of an experiment is its sample space. A single outcome can be a part of many different events. [4]
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
An event, however, is any subset of the sample space, including any singleton set (an elementary event), the empty set (an impossible event, with probability zero) and the sample space itself (a certain event, with probability one). Other events are proper subsets of the sample space that contain multiple elements. So, for example, potential ...
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.)
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 ...
The technique is wrong because the eight events whose probabilities got added are not mutually exclusive. One may resolve this overlap by the principle of inclusion-exclusion, or, in this case, by simply finding the probability of the complementary event and subtracting it from 1, thus: Pr(at least one "1") = 1 − Pr(no "1"s)