You are given a random exponential variable X: f(x) = λ exp(-λ x).
Suppose that X = Y + Z, where Y is the integral part of X and Z is the fractional part of X:
Y = IP(X), Z = FP(X).
Which is the following conditional probability:
P(Z < z | Y = n) for 0 ≤ z < 1 and n = 0, 1, … ?
The problem is as it follows:
"In cases more frequently considered, this set of possible values is a topologically discrete set in the sense that all its points are isolated points. But there are discrete random variables for which this countable set is dense on the real line (for example, a...
I have seen the following "extension" of discrete random variables definition, from:
pediaview.com/openpedia/Probability_distributions
(Abstract)
"... Equivalently to the above, a discrete random variable can be defined as a random variable whose cumulative distribution function (cdf)...
An abstract from:
"pediaview.com/Probability_distributions"
... Equivalently to the above, a discrete random variable can be defined as a random variable whose cumulative distribution function (cdf) increases only by jump discontinuities—that is, its cdf increases only where it "jumps" to a...
About the definition of "discrete random variable"
Hogg and Craig stated that a discrete random variable takes on at most a finite number of values in every finite interval (“Introduction to Mathematical Statistics”, McMillan 3rd Ed, 1970, page 22).
This is in contrast with the assumption that...