N-dimensional RV vs DT Random process

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Discussion Overview

The discussion centers on the differences and similarities between discrete random processes and N-dimensional random variables, exploring their definitions, interpretations, and handling in various contexts. The scope includes theoretical considerations and conceptual clarifications.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant suggests that a discrete random process can be viewed as a collection of random variables indexed by n, while an N-dimensional random variable consists of N random variables with a joint probability mass function (pmf).
  • Another participant points out that the primary difference lies in how these concepts are handled, mentioning that a sequence might be treated as a Markov process, where each variable depends on the previous one, unlike N-dimensional random variables which are typically studied as a single entity.
  • A later reply questions whether the differences are merely interpretative, seeking further clarification on any additional distinctions that might exist.
  • One participant asserts that context is the main point of differentiation, suggesting that there are no other significant differences beyond those already described.

Areas of Agreement / Disagreement

Participants express a general agreement that the two concepts are similar but interpreted differently. However, the discussion remains somewhat unresolved regarding whether there are additional differences beyond interpretation.

Contextual Notes

The discussion highlights potential limitations in understanding the nuances of how discrete random processes and N-dimensional random variables are defined and applied, particularly regarding context and interpretation.

dionysian
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If a discrete random process can be viewed as a collection of random variables indexed by a value n and a discrete N dimensional random variable can be viewed as N random variables with with a joint pmf. In these cases it seems like there is not much difference between a N dimensional random variable and a discrete time random process.

Know i am sure I am missing something very subtle but important here. I geuss me question is how is a discrete time random process diffrent than a n deminsional random varible?
 
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The difference is primary how they are handled. A sequence (for example) might be treated as a Markov process, where each variable is dependent on the value of the previous trial, but none before that. Also when dealing with a sequence, there is no limit on the number of terms, while treating it in n dimensions usually means the vector is studied as one entity.
 
Thanks for your reply mathman. So the two are very similar but they are just interpreted diffrently? Is there any diffrence other than that which someone might know about?
 
I can't fully understand your second question, but the point is there is nothing other than how I described it. Context is the main point.
 
Thanks mathman. I think I get it now.
 

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