Hi
I am not really a Statistician even though I get to teach the subject.
But I do enjoy playing with things, especially if I can find a way to
do it with (dare I say it --) an electronic spreadsheet!
This question concerns a straightforward linear system of
equations; there are n equations in n+1 unknowns.
I've just had a go at solving AX=B (for n=5 Matrices) for various
values of P(X=0) constraining solutions to obey 0<P(X=i)<1 for all i.
For n = 5,
A turns out to be invertible and looks like
-5 4 0 0 0
1 -5 4 0 0
0 1 -5 4 0
0 0 1 -5 4
1 1 1 1 1
B looks like
-p(0)
0
0
0
1-p(0)
Use Exel to find the inverse, then premultiply B with A(inverse),
using various p(0) values. For n=5 there are solutions availible, eg
with p(0) = 0.5 then p(1) = 0.178954.. etc . I haven't thought about
the general case yet.
> how do you solve a problem like this one?
> thanks in advance
> -------
> X is a chance variable such that X(omega)={1,2,3...,n}
> and for every i in {1,2,3...n}, 4P(X=i+2)=5P(X=i+1)-P(X=i)
>
> find the breakdown of X.
>
>
Cheers
------Martin/
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Martin James McKenzie
BSc(hons), MA, MSc, CTT
Academic Staff Member(ASM)
Lecturer in Mathematics and Statistics
Department of Business Studies
The WAIKATO POLYTECHNIC
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HAMILTON
NEWZEALAND
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