I am newly learner of subject of stochastic processes and my mind is full of questions. Hopefully I can ask one of them in a correct way.

Suppose that X is an random variable which follows exponential distribution with parameter $\lambda$. (Let's say X is number of the cars in the park) For a while of period lets say 30 days, I check the number of the cars and note the random values for day 1, D1=X1, D2=X2,...,D30=X30.

How can I compute the realization (x) of this random event?

With which concept ?

Can I do it Poisson process etc?

As I said, I am newly learner and all the informations are welcome.

Thank you.

  • 1
    $\begingroup$ Are the samples at the various times related, or independent? $\endgroup$ – Ian Mar 7 at 0:17
  • $\begingroup$ In the first step, we will consider they are independent . Thank you for your ideas in advance $\endgroup$ – Angelıque Mar 7 at 9:45
  • $\begingroup$ When they're independent, you just sample a bunch of random variables. It's not really a "process" until the variables become coupled. (Strictly speaking it is one of course, but hopefully you understand my meaning.) $\endgroup$ – Ian Mar 7 at 14:36
  • $\begingroup$ How can I calculate the realization if they are dependent? $\endgroup$ – Angelıque Mar 7 at 15:26
  • $\begingroup$ That depends on the character of the dependence. For example, for a Markov process, you need to retain the previous state in order to know how to sample the next state, but you can discard all previous information. $\endgroup$ – Ian Mar 7 at 15:29

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