Homework Help is Here – Start Your Trial Now!
Math
Statistics
You are given the measurements of two sides of a rectangle A and B with the associate errors A and σB, respectively. Assuming A and B are uncorrelated, calculate the error in the: > (i) sum A + B (ii) difference A - B (iii) the perimeter 2A + 2B (iv) the area A x B (v) the aspect ratio A/B

You are given the measurements of two sides of a rectangle A and B with the associate errors A and σB, respectively. Assuming A and B are uncorrelated, calculate the error in the: > (i) sum A + B (ii) difference A - B (iii) the perimeter 2A + 2B (iv) the area A x B (v) the aspect ratio A/B

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
See similar textbooks
icon
Related questions
Question
2.0.2 Problem 2: Error propagation a) You are given the measurements of two sides of a rectangle A and B with the associate errors A and B, respectively. Assuming A and B are uncorrelated, calculate the error in the: > (i) sum A + B (ii) difference A - B (iii) the perimeter 2A + 2B (iv) the area A x B (v) the aspect ratio A/B b) In the muon lifetime experiment, we obtain a histogram for the recorded decays as function of the time after the muon enters the detector. After binning the decays into discrete time bins, we expect the distribution of decays (histogram) to be described by an exponential function of time. Rather than fitting the data directly with an exponential function, it is sometimes more convenient to plot the logarithm of the decays in a bin (y;) as a function of time (x₁) and then fit a straight line to it. Each data point of the histogram (x, y) has a statistical error, oi √, associated with it. What happens to these errors when the semi-log histogram (x, log10 yi) is plotted? Assume that all values of y, are >> 1. = c) In a separate experiment, you find that log₁0 Eo = 1.5±0.5 (at 68% confidence level, CL). What is the value of Eo and the experimental bounds at 68% CL? (Note that 0.5 is not small compared to 1.5).
Transcribed Image Text:2.0.2 Problem 2: Error propagation a) You are given the measurements of two sides of a rectangle A and B with the associate errors A and B, respectively. Assuming A and B are uncorrelated, calculate the error in the: > (i) sum A + B (ii) difference A - B (iii) the perimeter 2A + 2B (iv) the area A x B (v) the aspect ratio A/B b) In the muon lifetime experiment, we obtain a histogram for the recorded decays as function of the time after the muon enters the detector. After binning the decays into discrete time bins, we expect the distribution of decays (histogram) to be described by an exponential function of time. Rather than fitting the data directly with an exponential function, it is sometimes more convenient to plot the logarithm of the decays in a bin (y;) as a function of time (x₁) and then fit a straight line to it. Each data point of the histogram (x, y) has a statistical error, oi √, associated with it. What happens to these errors when the semi-log histogram (x, log10 yi) is plotted? Assume that all values of y, are >> 1. = c) In a separate experiment, you find that log₁0 Eo = 1.5±0.5 (at 68% confidence level, CL). What is the value of Eo and the experimental bounds at 68% CL? (Note that 0.5 is not small compared to 1.5).
Expert Solution
Step 1

Note: As per the guidelines, in case of multiple questions, answer to first question will be provided. Kindly post other questions separately.

General formula for Error propagation:

If there are n measurements x1,x2, ...., xn with the uncertainties σ1, σ2,...., σn, and a function of the measurements fx1,...,xn is known, then the uncertainty in f is given by:

σf=∂f∂x1σ12+∂f∂x2σ22+....+∂f∂xnσn2

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
SEE MORE TEXTBOOKS