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    Uniform distribution

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    1.
    X_1,X_2,...,X_n are independent and uniformly distributed on [0,1]
    a. standardize X_1+X_2+...+x_n
    b. Give mgf of THE STANDARDIZED (a) sum.

    2. Suppose X is normal with mean u and variance sigma^2.
    P{u<= X <= u + 1.5 sigma}

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    https://brainmass.com/statistics/normal-distribution/uniform-distribution-variables-22706

    Solution Preview

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    1. are independent and uniformly distributed on [0,1]
    a. standardize
    b. Give mgf of THE STANDARDIZED (a) sum.
    (a) Solution. Since are independent and uniformly distributed on [0,1], we know that their means and variances are the same. and . So,

    ...

    Solution Summary

    This shows how to standardize the sum of variables and find the MGF.

    $2.49

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