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    Expected Value, Variance and Covariance of random variable

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    1. Say that E(X) = 10; and var(X) = 5. Find E(Y) and var(Y) in the following cases:
    a) Y = 0.37X - 3.79
    b) Y = 0.37X + 5.73
    c) Y = (3x^2+2)/4
    d) Y = aX + b

    2. Prove that:
    a) E(X^2) greater than equal to [E(X)]^2 (Hint: this follows immediately from the definition of the variance and from one of the properties of the variance).
    b) cov(X, Y ) = E(XY )- , where = E(X) and = E(Y ). (Hint: Use the definition
    of covariance).

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    https://brainmass.com/statistics/central-tendency/expected-value-variance-covariance-random-variable-119311

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    1. Say that E(X) = 10; and var(X) = 5. Find E(Y) and var(Y) in the following cases:
    a) Y = 0.37X - 3.79
    b) Y = 0.37X + 5.73
    c) Y = (3x^2+2)/4
    d) Y = aX + b

    Answer
    We have the result
    E(aX+b) = aE(X)+b
    V(aX+b) =a2V(X)

    a). ...

    Solution Summary

    Calculation of Expected Value E(X), Variance V(x) and Covariance of random variable.

    $2.49

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