Re: transformations of i.d. vars?
- From: Per Freem <perfreem@xxxxxxxxx>
- Date: Thu, 27 Sep 2007 19:24:14 -0000
On Sep 25, 10:15 pm, Richard Ulrich <Rich.Ulr...@xxxxxxxxxxx> wrote:
On Mon, 24 Sep 2007 19:25:12 -0700, Per Freem <perfr...@xxxxxxxxx>
wrote:
hello,
i am trying to understand how to analyze the distributions of random
variables under arbitrary transformations. if A and B are rv's and are
i.d. and i have some function f, then will f(A) and f(B) necessarily
have the same distribution? it seems to me that the answer is yes but
i failed to prove it and am not sure what tools one would use to prove
it.
here's an example. suppose A and B are distributed binomially with
n=10 and p=.5. suppose A measures the numbers of successes, and B the
numbers of failures. i can't possibly see how f(A) can be distributed
If A = 1-B, the two are *definitely* not independent.
And the log(A) is certainly different from the log(B),
but, if you are indeed letting A= 1-B, I can't tell what
you else may be asking. Looks like you are confused.
*differently* from f(B), given that both follow the same binomial
distribution... but again, im hoping someone can explain what a formal
proof of this would look like
--
Rich Ulrich, wpi...@xxxxxxxxxxxx://www.pitt.edu/~wpilib/index.html
i didn't say anything about independence, i said only i.d. -- sorry
for the confusion. they are only identically distributed, not i.i.d.
.
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- From: Per Freem
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- From: Richard Ulrich
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