1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    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!

Homework Help: Proof for expectation

  1. Jun 15, 2010 #1
    hello!
    can any1 please help me with the following proofs? thanks


    let X and Y be random variables. prove the following:
    (a) if X = 1, then E(X) = 1

    (b) If X ≥ 0, then E(X) ≥ 0

    (c) If Y ≤ X, then E(Y) ≤ E(X)

    (d) |E(X)|≤ E(|X|)

    (e) E(X)= [tex]\sum[/tex]P(X≥n)
     
  2. jcsd
  3. Jun 15, 2010 #2

    EnumaElish

    User Avatar
    Science Advisor
    Homework Helper

    What is the definition of expectation? Have you attempted any of these proofs?
     
  4. Jun 15, 2010 #3
    expectation is the expected value or mean.

    I have tried the first one using probability density function. but am not sure of my answer. while the others I have no idea how to attempt them

    thank you
     
  5. Jun 15, 2010 #4

    EnumaElish

    User Avatar
    Science Advisor
    Homework Helper

    Do you mind copying your answer for (a)?
     
  6. Jun 15, 2010 #5
    E(X) = [-∞]\int[/∞] g(x).f(x) dx

    let g(x) = X

    E(X) = [-∞]\int[/∞] 1.f(x) dx

    = 1. [-∞]\int[/∞] f(x) dx

    = 1


    P.S: [-∞]\int[/∞] is the integral of -infinity to infinity
     
  7. Jun 15, 2010 #6

    EnumaElish

    User Avatar
    Science Advisor
    Homework Helper

    Just a notational remark,
    should be E(g(x)). Other than this it looks right.

    What about (b)? Any ideas?
     
    Last edited: Jun 15, 2010
  8. Jun 15, 2010 #7
    ok thanks.

    nope...no idea for the second part
     
  9. Jun 15, 2010 #8

    EnumaElish

    User Avatar
    Science Advisor
    Homework Helper

    What is the definition of integral that you've been using?
     
  10. Jun 15, 2010 #9
    its the probability density function for a continuous distribution

    the integral gives the total area under the pdf
     
  11. Jun 15, 2010 #10

    EnumaElish

    User Avatar
    Science Advisor
    Homework Helper

    What are the characteristics of a pdf? Which conditions must hold for a function to be a pdf?

    For example, can f(x) = -1 for x = 0 to 1 be a pdf?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook