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Homework Help: Statistics basic question: Probability distrbution

  1. Feb 4, 2012 #1
    1. The problem statement, all variables and given/known data
    A random variable X has three, and only three, possible values, 0; 2; 4
    with the following probability distribution:

    Getting a 0 is 0:7

    Getting a 2 is 0:1

    Getting a 4 is 0:2

    Let X1 and X2 be two independent random variables with this distribution.

    (a) Determine the probability distribution for

    X(bar)2 = (X1 + X2)/2
    and use this distribution to determine the expectation and variance of X(bar)2

    (b) Determine the expectation and variance of X and verify that the
    variance of X(bar)2 is one-half the variance of X.

    2. Relevant equations

    3. The attempt at a solution

    X2(bar) = 0 with probability 0.49
    X2(bar) = 1 with probability 0.14
    X2(bar) = 2 with probability 0.29
    X2(bar) = 3 with probability 0.04
    X2(bar) = 4 with probability 0.04

    not sure how to work out the variance?

    Regards as always
    Last edited: Feb 4, 2012
  2. jcsd
  3. Feb 4, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You have the probability distribution of [itex] \bar{X}_2.[/itex] Just apply the _definition_ of variance and the formulas for it that you can find in any relevant book, or on-line if you look.

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