Make up to $500 this semester by taking notes for StudySoup as an Elite Notetaker Apply Now

Let R denote the resistance of a resistor that is selected

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Problem 25E Chapter 2.6

Statistics for Engineers and Scientists | 4th Edition

  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

4 5 0 352 Reviews
25
3
Problem 25E

Let R denote the resistance of a resistor that is selected at random from a population of resistors that are labeled 100 Ω. The true population mean resistance is μR = 100 Ω, and the population standard deviation is σR = 2 Ω. The resistance is measured twice with an ohmmeter. Let M1 and M2 denote the measured values. Then M1 = R + E1 and M2 = R + E2, where E1 and E2 are the errors in the measurements. Suppose that E1 and E2 are random with  and  Further suppose that E1, E2, and R are independent.

a. Find

b. Show that

c. Show that

d. Use the results of (b) and (c) to show that

e. Find

Step-by-Step Solution:

Answer :

Step 1 of 6:

            Let R denote the resistance of a resistor that is selected at random from a population of resistors that are labeled  

         Given, the true population resistance is ,

        and the population standard deviation

Let denote the measured values. Then = R + and = R + ,

   Where, and are the errors in the measurements.

Suppose that, are random with and

Step 2 of 6:   

a). To find

     That is,    

                             

                         

 

                              =

                           

                              = 2.2361

Similarly,

               

             

             

     

   

                         

               

                        =

                     

                       = 2.2361

  Therefore,

Step 3 of 6: 

b). To show that

       Then, 

                =        (where, = R + )

                         

                          =

                         = .             (since = )

      Therefore,  

                     =  

                     

                         Hence proved.

 

Step 4 of 6

Chapter 2.6, Problem 25E is Solved
Step 5 of 6

Textbook: Statistics for Engineers and Scientists
Edition: 4th
Author: William Navidi
ISBN: 9780073401331

×
Log in to StudySoup
Get Full Access to Statistics For Engineers And Scientists - 4th Edition - Chapter 2.6 - Problem 25e

Forgot password? Reset password here

Join StudySoup for FREE
Get Full Access to Statistics For Engineers And Scientists - 4th Edition - Chapter 2.6 - Problem 25e
Join with Email
Already have an account? Login here
Reset your password

I don't want to reset my password

Need help? Contact support

Need an Account? Is not associated with an account
Sign up
We're here to help

Having trouble accessing your account? Let us help you, contact support at +1(510) 944-1054 or support@studysoup.com

Got it, thanks!
Password Reset Request Sent An email has been sent to the email address associated to your account. Follow the link in the email to reset your password. If you're having trouble finding our email please check your spam folder
Got it, thanks!
Already have an Account? Is already in use
Log in
Incorrect Password The password used to log in with this account is incorrect
Try Again

Forgot password? Reset it here