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!

Would anyone explain the solution a little bit to me?

  1. Jun 14, 2015 #1
    • Member warned about posting without the template and with no effort
    I am preparing for my math probability class next semester. There is question: Calculate E(x3µσ) Would anyone explain the solution in the picture a little bit to me?

    1.Why is the step hold? Is there a formula or something that i can calculate E[X-µ]n?
    2.Why is the fourth step hold? Where is the σ from and why variance σ2= E[X-µ]2?
  2. jcsd
  3. Jun 14, 2015 #2


    User Avatar
    Gold Member

    If the distribution is continuous, then we have ## E[X^n]=\int X^n \rho(X) dX ##.
    Then it can be proved that ## E[aX+c]=aE[X]+c ## which can be used to prove the first formula.
    And variance is defined to be the expected value of the squared deviation from the mean, which means ## \sigma^2=E[(X-\mu)^2] ##.
  4. Jun 14, 2015 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Note that ##\sigma^2 \equiv \text{Var}(X)## is given by
    [tex] \begin{array}{cll} \text{Var}(X)& = E(X - \mu)^2 &\text{definition}\\
    & = E(X^2) - \mu^2 & \text{alternative formula}
    Therefore, we have ##E(X^2) = \sigma^2 + \mu^2##.

    To get the "alternative formula", just expand out ##(X - \mu)^2## and then take expectations.
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: Would anyone explain the solution a little bit to me?
  1. Explain A109598 to me? (Replies: 12)