Yes, you are correct. What we want for Problem 3 is to see how well SSLN
and CLT hold in finite samples. For Prob 3b, we are interested in how well
sample mean can approximate true mean in different sample sizes. So, you
want many simulations with different sample sizes: use a graph if you can.
Kosuke
---------- Forwarded message ----------
Date: Mon, 24 Feb 2003 21:53:59 -0500
To: kimai(a)fas.harvard.edu
Subject: Re: [gov2001-l] CLT (fwd)
Hi Kosuke,
One more question re: the binomial now that I've written my code & it seems
to work OK. I may be using the wrong verbiage, but I want to make sure
that, at a minimum, I have the concepts down. Is the following correct?:
A single random draw from the binomial distribution will return, for N
trials and given a probability pi, the number of successes for that random
draw. So, for each draw, there are N trials.
An experiment (or simulation, or whatever it should be called) simulates
multiple draws (N trials each) from the binomial. So, for instance, I
might run three experiments, one of which simulates 10 draws of N trials,
the second of which simulates 50 draws of N trials, and the third of which
simulates 100 draws of N trials (with N being held constant across the
three experiments). If I conduct enough of these experiments, I can test
to see whether the SLLN holds.
So, in other words, it is my understanding that an experiment consists of
multiple draws, that a draw consists of multiple trials, and that, to test
the SLLN, we should be conducting several different experiments (such that
each successive experiment consists of more draws than the one before, but
with the number of trials being held constant across draws/experiments).
To do this, I've used two loops in my code. This all seems logical to me,
and my output looks right, but I wanted to make sure that I'm thinking
about this correctly before I finish it.
Thanks.
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