Solved Problems In Probability

Solved Problems In Probability-83
must satisfy certain properties (it must be a -algebra) to qualify as a class of events.

must satisfy certain properties (it must be a -algebra) to qualify as a class of events.

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It must sound as an oxymoron - a computer (i.e., deterministic device) producing random events - numbers, in our case, to be exact.

See, if you can convince yourself that your computer can credibly handle this task also.

is an assignment with certain properties (it is a special kind of measure), called the probability function, or probability measure. We can interpret this as saying that the event of getting Heads, and the event of getting Tails, each take up an equal half of the set of possible outcomes; the event of getting Heads or Tails is certain, and likewise the event of getting neither Heads nor Tails has probability 0.

Of course, to understand this example doesn't need measure theory, but it does show how to translate a very basic situation into measure-theoretic language.

Every second it will pick up one of the three numbers - 1, 2, or 3.

You can terminate the process anytime by pressing the "Stop" button.When a coin is tossed, there are two possible outcomes: The Sample Space is all possible Outcomes (36 Sample Points): ...The Event Alex is looking for is a "double", where both dice have the same number. Many events can't be predicted with total certainty.The best we can say is how likely they are to happen, using the idea of probability.Interestingly, a recent book by Marilyn vos Savant dealing with people's perception of probability and statistics is titled . As with other mathematical problems, it's often helpful to experiment with a problem in order to gain an insight as to what the correct answer might be.By necessity, probabilistic experiments require computer simulation of random events.The foundations of probability reside in an area of analysis known as measure theory.Measure theory in general deals with integration, in particular, how to define and extend the notion of "area" or "volume." Intuitively, therefore, probability could be said to consider how much "volume" an event takes up in a space of outcomes.American Heritage Dictionary defines Probability Theory as the branch of Mathematics that studies the likelihood of occurrence of random events in order to predict the behavior of defined systems.(Of course is a question that is not all that simple to answer.) Starting with this definition, it would (probably :-) be right to conclude that the Probability Theory, being a branch of Mathematics, is an exact, deductive science that studies uncertain quantities related to random events.


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