Calculating Error for Measuring y3 in Range x1 to x2

[Doctor Luz]

Suppose I have some measures of certain physical magnitude "I" between the range x=x1 and x=x2.

I have for each x in this range a value y of I, then y=I(x)

I have a continuous level of noise y=y1.

I have I(x3)=y3 with x1<=x3<=x2.

how can I compute the error measuring y3?

Thank you

 

[HallsofIvy]

If I read this correctly then I(x) is a function of x for x between
x1 and x2. You then say "I have a continuous level of noise y=y1."
That's a bit confusing. Is y1 a constant? Since you had already used y to represent the value of the function I(x), do you intend y1 to be a noise on the value of I(x) or on x itself? I doubt that you intend the former since that in that case the answer would be, of course, y1. If you intend the latter, then, since relationship between the error in x and the error in y= I(x) depends heavily upon the function I, there is no general formula.