Division of a number by another with standand deviation

• Oct 31st 2012, 04:44 AM
Pableim
Division of a number by another with standand deviation
Hi guys,

Can you help me please, with the following operation, which has an standard deviation value on the denominator?

A=0.5
B=5.55(+/- 0.02)

What is the solution of C=A/B ?

Regards,

Pablo

PD. Please, explain the step by step resolution of the problem.
• Oct 31st 2012, 05:23 PM
chiro
Re: Division of a number by another with standand deviation
Hey Pableim.

You are trying to find C = A/[5.55 +- 0.02].

Now factorize this and we get:

C = [A/5.55]/[1 +- 0.02/5.55]
Let X = A/5.55, R = 0.02/5.55: Now you have something in the form of

C = X * [1 / (1 +- R)].

So in terms of standard errors this is what you have.

However: if you want to look at the above quantity in terms of a distribution then you need to find the PDF of the ratio of those two variables and if A and B are normal then you will get a Normal Ratio Distribution.
• Nov 1st 2012, 02:43 AM
Pableim
Re: Division of a number by another with standand deviation
Hi Chiro,

Doing your suggestion, the answer was [0.5/(5.55+/-0.02)], applying standar deviations operations rules, like the ones observed in Multiplication and Division of Values with Standard Deviation . But I need only a number as a solution, for example, 0.0005+/-0.0004. Is there a way to obtain an answer like the example?.

By the way, you introduce somethig about like "to find the PDF of the ratio of those two variables". Please, explain to me What are you mean?

Regards
Pablo.
• Nov 1st 2012, 02:57 AM
chiro
Re: Division of a number by another with standand deviation
A ratio distribution is just a random variable where Z = X/Y and X,Y are random variables.

There have been worked out cases like when X and Y are normal distributions where you can get a PDF for Z.