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Math Help - Mean/Var of RV of Averaged Random #s

  1. #1
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    Mean/Var of RV of Averaged Random #s

    I'm trying to find the mean and variance of a random variable which is the average of 4 random numbers from a uniform distribution between 0 and 1. Anyone know how to go about finding this? Any help would be much appreciated.

    Thanks!
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  2. #2
    MHF Contributor matheagle's Avatar
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    E(X_i)=1/2 for all i

    Thus E(\bar X)=1/2 even without independence

    Likewise V(X_i)=1/12 for all i, that's {(b-a)^2\over 12}

    So V(\bar X)=V(X_i)/n={1\over 12n}={1\over 48} where we need independence here
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