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Problems and Solutions in Mathematical Finance: Stochastic Calculus, Volume I by Eric Chin, Sverrir Olafsson, Dian Nel

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  1. 17. Bivariate Normal Distribution Property. Let c01-math-656 and c01-math-657 be jointly normally distributed with means c01-math-658, c01-math-659, variances c01-math-660, c01-math-661 and correlation coefficient c01-math-662 such that the joint density function is
    equation

    Show that

    equation

    Solution

    By definition

    equation

    where c01-math-663 and c01-math-664.

    For the case we have

    where which is the probability density function ...

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