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Mathematics is an extremely interesting subject if it is understood and analyzed well. However, this conceptual understanding is where most students fail. There is deep hidden logic in each and every, step, law, theorem, hypothesis, etc. But, when students try to overlook the logics and try to memorize they end up in trouble. One such logically neglected part in statistical mathematics is the ergodic theorem. Hence, we have with us Ergodic Theory assignment help.
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Before understanding this subject precisely, one first has to know about probability theory. What is probability? It is the chance of an event. But, how is it calculated. In mathematics, statistics and other science subject, there can be three cases of situations regarding events:
- Where the number of events can be counted each and are finite in number
- Where they may be counted, but there are infinite number of those possibilities
- Where they cannot be counted and are distributed in form of a continuous set.
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In the first case of event arrangements, we get probability of an event by dividing the number of favorable events by total number of possible events.
In the second case, we can get a non-zero probability only if there are a hugely many number of favorable events. In such situations, we apply concepts of limits and arrive at an answer.
In third case, however the approach has to be quite different than simple division. Then we have to use probability density functions.
Now, probability need not be constant. It might so happen that they change with time and position. Such cases mostly occur with probabilities of the third kind discussed above and they are quite common in physics and chemistry.
Ergodic theory deals with such probabilities and it states that the average of probabilities over all possible space is equal to its average taken over a long period of time.Mathematically, <Probability>all space=<Probability>time (t=0 to ). A limiting relation exists between them.
It is physically very important, because it says that the results given by a huge number of events happening altogether in a certain region of space is the same as the result of those events happening each one by one over a long period of time. If you still cannot get this idea properly come to our Ergodic Theory assignment help.
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