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Probability with expectation and variance

  1. Oct 23, 2012 #1
    A robot arm solders a component on a motherboard. The arm has
    small tiny errors when locating the correct place on the board. This
    exercise tries to determine the magnitude of the error so that we know
    the physical limitations for the size of the component connections. Let
    us say that the right place to be soldered is the origin (0,0), and the
    actual location the arm goes to is (X,Y ). We assume that the errors
    X and Y are independent and have the normal distribution with mean
    0 and a certain standard deviation sigma.
    (a) What is the density function of the distance
    D = SQRT ( X^2 + Y^2)

    (b) Calculate its expected value and variance:
    E(D) and Var(D)

    (c) Calculate
    E[|X^2 - Y^2|]

    Ok so I changed to polar and have my joint pdf as follows:

    (r/sigma^2) * e^(-r^2/2sigma^2) *1/2pi

    Don't know how to calculate expectation and variance. I think I'm doing it wrong
  2. jcsd
  3. Oct 23, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Please show your attempt.
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