Hi,
I work on a real life problem with roundoff errors and found a glitch in my thinking. If someone knows how to solve this problem I appreciate it.
The problem:
I have a container with n objects inside. I can weight the full container (Q), individual objects () and the empty container ().
We have then that:
The scale round the weight to the nearest integer.
Then I have measures (Empty container, Full container and n objects)
for i:0..n
where and are random variables iid (here it is my error - see Note)
I want measure de difference between and
I'm going to find
Defining
We have that is
Then is a sum of n + 2 iid random variables
Note: is integer then is not independent from
By Central Limit theorem:
In this case has and
Then
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I think I solved it.
Take a look at the next table
Note that don't afect the final error. I only need to work with rounded to the nearest integer (fourth column).
Then
Where is a sum of iid random variables
Applying Central Limit Theorem, we obtain this aproximation
I think this is right
Last edited by jcarne; 03-23-2017 at 04:49 PM. Reason: We want Prob than an error is greater or equal than current error
logistiquecim (05-01-2017)
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