Cumulative Distribution Function for Sum of Continuous Distributions
That means $X\in x$ is a partition of $X+Y$? But how could that be? It only accounts for the $X$ part.
Asked
Active
Viewed 219 times
2
-
The notion of a partition of $X+Y$ doesn't make sense. The partition is of the space of all outcomes. And the different possible values of $X$ (irrespective of the values of $Y$) do partition the space of outcomes: for each outcome, $X$ takes some value, and any two outcomes on which the value $X$ takes differ are different outcomes. – spaceisdarkgreen Mar 17 '18 at 23:59
-
@spaceisdarkgreen I see, so for any value of $X$, there is only 1 value $Y$ could possibly be to satisfy $T = X + Y$. Thus, possible values of $X$ partitions $T$? – A_for_ Abacus Mar 18 '18 at 19:12
-
As I said, partitioning a random variable isn't a really a concept that makes sense. This has nothing even to do with what $T$'s definition is in terms of $X$. The application of LTP would be valid if $Tle t$ were replaced by literally any event. – spaceisdarkgreen Mar 18 '18 at 22:43