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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. 12. Chi-Square Distribution. Show that if c01-math-534 then c01-math-535.

    Let c01-math-536, c01-math-537, c01-math-538, c01-math-539 c01-math-540 c01-math-541 be a sequence of independent and identically distributed random variables each following a standard normal distribution. Using mathematical induction show that

    equation

    where c01-math-542 has a probability density function

    equation

    such that

    equation

    Finally, show that and ...

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