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    Partial Differential Equations and Probability Density Functions

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    Please see the attached file for the fully formatted problems.
    1) Suppose that S is a random variable that is defined on [0,∞) and whose probability density function is:

    (see the attached file)

    a and b being positive numbers. Show:


    (see the attached file)

    2) We know that the solution of the final value problem

    (see the attached file)

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    Solution Summary

    Partial differential equations and PDFs are investigated.