Answer:
= - 7n - 1
Step-by-step explanation:
There is a common difference between consecutive terms , that is
- 15 - (- 8) = - 22 - (- 15) = - 29 - (- 22) = - 36 - (- 29) = - 7
This indicates the sequence is arithmetic with nth term
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 8 and d = - 7 , then
= - 8 - 7(n - 1) = - 8 - 7n + 7 = - 7n - 1
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.