Notices
Results 1 to 1 of 1

Thread: Can't solve Question on probability density

  1. #1 Can't solve Question on probability density 
    New Member
    Join Date
    May 2013
    Posts
    4
    I was reading Introduction to quantum Mechanics [1st edition] by David Griffiths and was doing some exerciese, then I'm stuck on Problem 1.4.

    Problem 1.3 The needle on a broken car speedometer is free to swing, and bounces perfectly off the pins at either end, so that if you give it a flick it is equally likely to come to rest at any angle between 0 and π.

    (c) Compute <sin
    θ>,<cosθ>, and <cos2θ>

    Problem 1.4 We consider the same device as the previous problem, but this time we are interested in the x-coordinate of the needle point -- that is, the "shadow", or "projection", of the needle on the horizontal line.

    (a) What is the probability density
    ρ(x)? [ρ(x) dx is the probability that the projection lies between x and (x+dx).] Graph ρ(x) as a function of x, from -2r to +2r, where r is the length of the needle. Make sure the total probability is 1. [Hint: You know (from Problem 1.3) the probability that θ is in a given range; the question is, what interval dx corresponds to the interval dθ?]

    (b) Compute <x>(average of x), <x2>(average of x), and
    σ (standard deviation) for this distribution. Explain how you could have obtained these results from part (c) of problem 1.3.

    Thank you for reading this, and if you don't bother, please give me some hints to solve this, I'm getting a headache.


    Reply With Quote  
     

  2.  
     

Similar Threads

  1. Replies: 0
    Last Post: May 30th, 2012, 03:05 PM
  2. probability density
    By 15uliane in forum Physics
    Replies: 4
    Last Post: July 9th, 2011, 03:59 PM
  3. Density and Floating Question
    By AlphaParticle in forum Physics
    Replies: 3
    Last Post: April 8th, 2011, 10:41 PM
  4. interpolating between probability density functions
    By Timoshenko in forum Mathematics
    Replies: 0
    Last Post: October 19th, 2009, 10:05 AM
  5. Change in Probability Density Function
    By Drewau2005 in forum Mathematics
    Replies: 1
    Last Post: April 13th, 2007, 04:36 AM
Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •