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    Mixing the Constant with the Normal

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    Please see the attached file.
    There is a minor typo in the part(d).
    The function should be 1/(b-a), not 1/(a+b).

    From Conditional distribution and the Bivariate Normal distribution.
    Please show each step of your solution and check your final answer.
    Thank you.

    © BrainMass Inc. brainmass.com December 24, 2021, 7:06 pm ad1c9bdddf
    https://brainmass.com/math/probability/mixing-constant-normal-162855

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    Solution. By (b), we know that for all

    ,

    where c and d are constants.

    By (c), we know that

    which is a constant independent of t.

    Then by a), b) and c), we can write the conditional probability density function as follows.

    ................(*)

    Note 1): (*) shows that the conditional probability distribution is a normal distribution with mean ct+d and standard deviation as stated in (b) and (a).

    Note 2): exp(x) denotes the exponential function

    By d), we know that the marginal distribution in X is

    So, by a formula for the joint p.d.f.: , we can get the joint p.d.f. as follows. For every real number y,

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 7:06 pm ad1c9bdddf>
    https://brainmass.com/math/probability/mixing-constant-normal-162855

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