# Uncorrelated uncertainties for W with x=4.2(0.2) and y=0.7(0.1)

• bocobuff
In summary, the question asks for the values and uncertainties of W in standard format, with x=4.2(0.2) and y=0.7(0.1). The solution involves taking the partial derivatives of W with respect to x and y, and using them in a formula to calculate the uncertainty of W.
bocobuff
1. Homework Statement
For uncorrelated uncertainties LaTeX Code: \\delta x and LaTeX Code: \\delta y give the values and uncertainties for W in standard format.
A.) W=x+y with x=4.2(0.2) and y=0.7(0.1)

2. Homework Equations

3. The Attempt at a Solution
well i think i am supposed to take the partial derivatives of W with respect to x and y (dW/dx and dW/dy) which both =1. Then is the total derivative DW/DXorY = 1+1 dx/dy? Or do I only use the derivatives for the uncertainties and just plug x and y, 4.2 and 0.7, into W?

If you have a function $f(x_1, x_2, \cdots, x_n)$ where all the variables $x_i$ have their own uncertainty $\Delta x_i$, then what is the central value for f?
For the uncertainty there is a formula which involves the partial derivatives, but it's not what you seem to think it is. IIRC it is
$$(\Delta f)^2 = \sum_{i = 1}^n \left( \frac{\partial f}{\partial x_i} \Delta x_i \right)^2$$
but you can probably look that up in your textbook.

## 1. What are uncorrelated uncertainties?

Uncorrelated uncertainties refer to the uncertainties in different variables or measurements that are not related or dependent on each other. This means that changes in one variable do not affect the uncertainties in another variable.

## 2. How are uncorrelated uncertainties calculated?

Uncorrelated uncertainties are typically calculated by taking the square root of the sum of the squares of the individual uncertainties. This is known as the root-sum-square method or RSS method.

## 3. Can uncorrelated uncertainties be converted to correlated uncertainties?

Yes, uncorrelated uncertainties can be converted to correlated uncertainties if there is a known relationship or dependence between the variables. This can be done using statistical methods such as regression analysis.

## 4. What is the significance of uncorrelated uncertainties in scientific experiments?

Uncorrelated uncertainties play a crucial role in scientific experiments as they help to quantify the level of uncertainty in measurements and results. This information is important for evaluating the reliability and accuracy of the experiment.

## 5. How can uncorrelated uncertainties affect the interpretation of experimental data?

Uncorrelated uncertainties can affect the interpretation of experimental data by introducing errors and inaccuracies. It is important to account for these uncertainties in data analysis to ensure the validity and accuracy of the conclusions drawn from the experiment.

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