# Thread: Probability and roundoff errors

1. ## Probability and roundoff errors

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

--------------------------------------------------------------------------------------------------------------------------------------------------------------------------

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

2. ## Re: Probability and roundoff errors

I think I solved.

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

Then

Where is a sum of iid random variables

3. ## The Following User Says Thank You to jcarne For This Useful Post:

logistiquecim (05-01-2017)

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