In my readings, I've come across unbounded discrete probability
functions, e.g.
f(x) = (1/2)^x, x = 1,2,3...
= 0 elsewhere
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?
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?
Any help will be appreciated.
Thanks.
-dw
.
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