"Understanding Random Process X(t) and Its Sample Realizations

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Homework Help Overview

The discussion revolves around understanding the random process X(t) defined as a constant C, where C is uniformly distributed over the interval [-5, 5]. Participants are exploring the implications of this definition on the nature of sample realizations of the process.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the assumption that all sample realizations will appear the same, with some suggesting that C can take on various values within the specified range, rather than being constant. There is a focus on the implications of the uniform distribution and the nature of the probability density function (PDF).

Discussion Status

The discussion is active, with participants challenging initial assumptions about the behavior of the random variable C. Some have provided clarifications regarding the uniform distribution and its implications for sample realizations, leading to a reevaluation of earlier statements.

Contextual Notes

There is a noted confusion regarding the interpretation of the constant value of C in relation to its uniform distribution, as well as the implications for sketching sample realizations. Participants are navigating these misunderstandings without reaching a definitive conclusion.

marina87
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Problem statement: Define the random process X(t) = C where C is uniform over [-5,5].

a) Sketch a few sample realizations


I need reassurance that if I do a a few sample realizations of this random process they are all going to look the same. They are going to be an horizontal line with x(t) constant equal to 1/5.

I see how this random process is define and it doesn't depend of time. Its a WSS process
 
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marina87 said:
Problem statement: Define the random process X(t) = C where C is uniform over [-5,5].

a) Sketch a few sample realizations


I need reassurance that if I do a a few sample realizations of this random process they are all going to look the same. They are going to be an horizontal line with x(t) constant equal to 1/5.

I see how this random process is define and it doesn't depend of time. Its a WSS process

Why would you think that C always comes out equal to 1/5?
 
Ray Vickson said:
Why would you think that C always comes out equal to 1/5?

Because I understood that C is a random variable with uniform distribution over [-5,5]. The PDF is 1/(5-(-5)). That is 1/10 and not 1/5.
 
marina87 said:
Because I understood that C is a random variable with uniform distribution over [-5,5]. The PDF is 1/(5-(-5)). That is 1/10 and not 1/5.

Yes, C~U(-5,5). You are saying that C must always come out equal to either 1/5 (or maybe 1/10)! So, you are saying that C can never equal 3, or -2, or 4.5, or any other number in (-5,5). Do you honestly believe that?
 
Ray Vickson said:
Yes, C~U(-5,5). You are saying that C must always come out equal to either 1/5 (or maybe 1/10)! So, you are saying that C can never equal 3, or -2, or 4.5, or any other number in (-5,5). Do you honestly believe that?

@Ray I was very wrong. If I sketch a sample realization for x(t)=C with C been uniform over [-5,5] I will have for example a realization with a horizontal line in x1(t)=-5 (the y-axis) another realization can be x2(t)=2.5 with a horizontal line in 2.5 from t>=0.

Am I right?
 

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