Re: Probability question


Bill Howells wrote:
Eh, not that long ago, just a beginner. But if I can't do a simple
binomial probability, I'd better hang it up right now!

Bigw, you made me curious with the Poisson,

which is me, in French.

which I had to check. But
it looks like the Poisson distribution is derived from the Binomial by
letting n -> infinity

Much more than that requirement. :-)

so with n=4, it is probably not a good
approximation. I calculated with a Poisson mean of lambda = n*p =
4*(2/3) and a count of k=3 events, I get a Poisson probability of about
0.18. Contrast this with the p = 32/81 = 0.395 from the Binomial, and
you can see the Poisson is not working very well.

That's another pain in the neck and time-wastin' rules of thumbs
in textbooks written by author who had nothing better to do.

Discrete Poisson probabilities no matter how many terms or how
large or small n is, can always be equated EXACTLY to an
equivalent tail probability of a well-known continuous random
variable.

I am purposely leaving out all the details of the correspondence.

-- Bob. Le poisson; ou poissons de récif

.

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