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

[marina87]

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

 

[Ray Vickson]

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?

 

[marina87]

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.

 

[Ray Vickson]

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?

 

[marina87]

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?