Probability and uncertainties

[Niles]

Homework Statement

Hi all.

Lets say i have some data points (x, y) (we will call these data 'D'). There is no uncertainty in x, and the uncertainty in y is 1.

I believe t hat x and y are connected as y = ax², and I want to find the probability of a having a certain value given the data D.

The Attempt at a Solution

I know how to find the probability of y having some specific value given some data points for y with an uncertainty. But in this case, x and y are connected by a. I thought that perhaps the relative unvertainty in y is the same for a?

Thanks in advance.


Niles.

 

[mighty2000]

Dear Niles,

Thank you for sharing your question with the community. It is always exciting to see scientists exploring new ideas and seeking answers to challenging problems.

Based on the information you provided, it seems that you are trying to determine the probability of a certain value for the parameter a in the equation y = ax2, given a set of data points (x, y) with an uncertainty of 1 in y. In this case, the relative uncertainty in y does not necessarily correspond to the uncertainty in a. This is because the uncertainty in y depends on both the uncertainty in a and the value of x. Therefore, in order to determine the probability of a given value for a, you will need to consider both the uncertainty in y and the relationship between a and x.

One approach you could take is to use Bayesian statistics, which allows you to update your belief about the value of a based on new data. In this case, your prior belief about the value of a could be based on previous knowledge or assumptions, and then updated with the new data points (x, y). This will give you a posterior distribution for a, which represents the probability of a taking on different values given the data D.

I hope this helps and wish you all the best in your research.