Discrete-time discrete-valued random process

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SUMMARY

The discussion centers on a discrete-time discrete-valued random process defined by three sequences, each chosen with equal probability of 1/3. The participants analyze whether this process exhibits properties such as being independent and identically distributed (i.i.d), independent increments, stationary, or wide-sense stationary. It is concluded that the process is not i.i.d due to the dependence on the chosen sequence, and it is also not stationary as the statistical properties change over time. Definitions of the properties are essential for a comprehensive understanding of the analysis.

PREREQUISITES
  • Understanding of discrete-time random processes
  • Knowledge of statistical properties: i.i.d, independent increments, stationary, wide-sense stationary
  • Familiarity with probability theory and random variables
  • Ability to interpret sequences and their implications in stochastic processes
NEXT STEPS
  • Study the definitions and implications of i.i.d random variables
  • Explore the concept of independent increments in stochastic processes
  • Research stationary processes and their characteristics
  • Examine wide-sense stationary processes and their applications
USEFUL FOR

Students and professionals in statistics, data science, and applied mathematics who are analyzing random processes and their properties.

jandson
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I have the random process:

Sequence 1: 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 ...
Sequence 2: 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 ...
Sequence 3: 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 ...

where let nature choose one of these sequences at random with equal probability 1/3.

Can we say anything about this process being i.i.d, independent increments, stationary or wide-wense stationary?
 
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jandson said:
Can we say anything about this process being i.i.d, independent increments, stationary or wide-wense stationary?

Since you defined a specific process, you can give a definite yes-or-no answer to each of those properties.

I think you should at least quote the definitions of the properties you are interested in. Even if your post is not intended as a "homework type" question, it would make a good one.
 

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