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A single outcome may be an element of many different events, [2] and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. [3] An event consisting of only a single outcome is called an elementary event or an atomic event; that is, it is a singleton set.
If the outcome is the element of the elementary event of two pips on the first die and five on the second, then both of the events, "7 pips" and "odd number of pips", are said to have happened. The probability measure P {\displaystyle P} is a set function returning an event's probability .
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]
The problem concerns two envelopes, each containing an unknown amount of money. The two envelopes problem, also known as the exchange paradox, is a paradox in probability theory. It is of special interest in decision theory and for the Bayesian interpretation of probability theory. It is a variant of an older problem known as the necktie paradox.
In this case a set of dummy variables is constructed, each dummy variable having two mutually exclusive and jointly exhaustive categories — in this example, one dummy variable (called D 1) would equal 1 if age is less than 18, and would equal 0 otherwise; a second dummy variable (called D 2) would equal 1 if age is in the range 18–64, and 0 ...
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Switching {X,Y} in a graph. A two-graph is equivalent to a switching class of graphs and also to a (signed) switching class of signed complete graphs.. Switching a set of vertices in a (simple) graph means reversing the adjacencies of each pair of vertices, one in the set and the other not in the set: thus the edge set is changed so that an adjacent pair becomes nonadjacent and a nonadjacent ...
However, the league-mandated deadline to apply for a number swap had passed by the time of Monk’s departure, forcing Ball to wear No. 2 once more during his All-Star second season. View this ...