[EMAIL PROTECTED] (driver_writer) wrote in message
news:<[EMAIL PROTECTED]>...
> In my readings, I've come across unbounded discrete probability
> functions, e.g.
>
> f(x) = (1/2)^x, x = 1,2,3...
> = 0 elsewhere
Terminology correction:
Bounded discrete density function (0 <= f(x) <= 0.5) on an
unbounded domain.
> How does one take the Expected value or a r.v. X, for an unbounded (or
> in this case bounded on the left side) p.f?
E(x) = SUM(x=1,oo){ x*f(x) }
> My guess is you have to see if the series converges or diverges. If it
> converges, you take the sum and then ?
>
> Also, in order to take the mode of the distribution, for the
> continuous pdf you can find the maximum by taking the derivative,
> setting it to 0 and solving. How would you find the mode for a
> discrete p.f like the one above?
Compare it to the corresponding continuous value pdf.
f(x) = exp(-a*x), x=1,2,...
a = ln{2} = 0.693...
Hope this helps.
Greg
.
.
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