Some Paradox on Confidence Interval on Population Parameter!

Fellow experts who have been patiently guiding me from my past
messages are aware that I am looking into the confidence interval
stuffs.

Frequentist View:
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- Population unknown parameter (lets say mean-mu) is a constant value.
- From drawn sample, we compute the sample mean
- We use the sample mean and confidence interval on mu to get some
understanding of the Population unknown parameter.

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Question:
What if my data are actual population data. That is, no sampling is
involved.
Lets say my population is the entire traffic light in my city, N.
I have on hand the daily number of malfunction traffic lights, Xi,
where i represents 'day'

I am interested in the parameter Y of the population, which is the
daily average traffic light malfunction:
Yi = Xi / N

For example on day 1, X1 = 10 and population N = 10000:
Y1 = 10/10000 = 0.001

Now, Y1 is population parameter.

(Q1) Should it have a confidence interval?
(We know that the meaning of 90% confidence interval is that if we
repeat the same experiment many many times and get many many
intervals, 90% of the intervals will contain the population
parameter).
Since there is no way of doing another resampling for Day 1. Also,
based on frequentist view, Population parameter is CONSTANT, which
means it SHOULD NOT have an interval.

But on Day 2, X2 = 14: Y2 = 0.0014

(Q2) Shouldn't Population parameter be constant? But Y1 not equal Y2.

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My explainations:

(1) Perhaps Y1 is INDEED the true value of the population paramter by
valid for Day 1 only. On Day 2, its Population parameter value
changes. Therefore Y1 and Y2 should not have a Confidence Interval.

Hence Daily Yi differs mainly due to a shift in the actual value of
the population parameter overtime.

~~~But how to DETECT that it has REALLY shift? and not merely random
dispersion?~~~

(2) Rather than taking frequentist view, A Bayesian approach will
avoid the paradox. In bayesian interval, the assumption is that
population parameter are NOT constant, it has a distribution. This
explains why Y1 and Y2 are different.

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What do you think?

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