Answer:
See the proof below.
Step-by-step explanation:
For this case we need to proof that: Let be independent random variables with a common CDF
. Let
be their ECDF and let F any CDF. If
then
Proof
Let different values in the set {
} and we can assume that
represent the number of
that are equal to
.
We can define and assuming the probability
.
For the case when for any
then we have that the
And for the case when all and for at least one
we know that
for all the possible values
. So then we can define the following ratio like this:
So then we have that:
And the log for a number is 0 or negative when the number is between 0 and 1, so then on this case we can ensure that
And with that we complete the proof.