Re: Independent Random Varaible


mxkdirs@xxxxxxxxx wrote:
hi....this is a matlab question...we know that in a poisson process for
any pair of non-overlapping intervals (to,t1] and (t2, t3], number of
arrivals in each interval N(t1)-N(to)and N(t3)-N(t2) are independent
random variables. now I want to show this in matlab. i've a poisson
process (with 50 samples) and each sample is upto maximum time of 10
(seconds or any unit). Now if i pick two time intervals, for example,
(0,3] and (5,8] and count the number of arrivals in each of these
intervals {a = N(3)-N(0) and b = N(8)-N(5)} I need to show that a and
be are independent random variables.

With a finite number of samples and a numerical experiment,
the best you can do is to show consistency with independence.

I think I can convince myself that if a and b are independent, then
the covariance cov(a,b) should be equal to zero. That is the
off-diagonal terms of the results of Matlab call COV(a,b).

However:
- for a finite sample, it will be small but nonzero.
- you might want to show that it tends to zero as the sample
size increases
- covariance = 0 does not necessarily imply independence.

- Randy

.

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