Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A Mean volume of sphere (normal distributed radius)

  1. Jun 24, 2016 #1

    ChrisVer

    User Avatar
    Gold Member

    I read in http://www-library.desy.de/preparch/books/vstatmp_engl.pdf page 29 (43 for pdf) that the mean volume is:
    [itex]<V> = \int_{-\infty}^\infty dr V(r) N(r| r_0,s)[/itex]
    I have two questions.
    Q1: why do they take the radius to be from -infinity to +infinity and not from 0 to infinity?
    Q2: is there an intuitive way to see/describe why the mean volume is larger than the one obtained from the mean radius?

    Thanks
     
    Last edited: Jun 24, 2016
  2. jcsd
  3. Jun 24, 2016 #2

    Charles Link

    User Avatar
    Homework Helper

    It would appear the normal distribution about ## r=r_o ## is an approximation they want you to use even though that allows for a finite probability that ## r<0 ##. The integral from minus infinity to plus infinity can be solved in closed form, but I don't believe you get a closed form if the limits were zero to infinity even though the answer would be nearly identical. The ## V=(4/3) \pi r^3 ## function will add more weight to the larger r's because of the 3rd power dependence, making the mean volume larger than ## V=(4/3) \pi r_o^3 ##, but I don't have a simple intuitive description for that.
     
  4. Jun 25, 2016 #3

    Stephen Tashi

    User Avatar
    Science Advisor

    You could compare the mean of ##\{1^3, 2^3, 3^3\} ## with ##2^3##.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Mean volume of sphere (normal distributed radius)
  1. Normal distribution (Replies: 7)

  2. Normal distribution (Replies: 7)

  3. Normal Distribution (Replies: 4)

  4. Normal distribution (Replies: 3)

Loading...