1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Expected Value and integration

  1. Mar 19, 2010 #1
    1. The problem statement, all variables and given/known data

    Suppose that 15 observations are chosen at random for the pdf f(Y) = 3y^2 on the interval 0 to 1. Let X denote the number that lie in the interval (.5,1). Find E(X)

    2. Relevant equations

    3. The attempt at a solution

    Ok so to get the expected value u integrate the pdf times the random variable.
    Doing this is the integral 3y^3 and it turns to .75y^4

    This is where I get confused. First of all I thought that it would have summed to 1 so that the number of X on that range would be 15, but it cant be it would be 11.25

    Aside from that, to find the number over this range i kno is 15x the expected value but i cant figure out the bounds. Is it the value of 0,1 - the value of .5,1 or something else all together

    Thanks in advance
  2. jcsd
  3. Mar 20, 2010 #2


    Staff: Mentor

    Try to be more consistent in your use of variables. You are using x and y interchangeably, and that's bound to lead to confusion.

    [tex]E(x) = \int_{0.5}^1 3x^2 dx[/tex]

    You got the right antiderivative, but you should be working with a definite integral. Since you're concerned only with the interval [0.5, 1], you should expect the expected value to be a number somewhere in that interval.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook