Exercise 5.9 Suppose that Z = (Z1,Z2, . . . ,Zn) follows the n-variate standard normal distribution.

Question:

Exercise 5.9 Suppose that Z = (Z1,Z2, . . . ,Zn) follows the n-variate standard normal distribution. Prove the following.

(1) Show that the moment generating function of Z is given by

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(2) Suppose that X has mean vector = (μ1, μ2, . . . , μn) and covariance matrix Σ = (σij ). Let C be such that Σ = CC ⊤
. Show that X = +CZ.
(3) Obtain the MGF (5.29) for X.

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Stochastic Processes With Applications To Finance

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Authors: Masaaki Kijima

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Question Posted: Sep 19, 2024 07:03 PM

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Exercise 5.9 Suppose that Z = (Z1,Z2, . . . ,Zn) follows the n-variate standard normal distribution.

Question:

mz(t) = exp t = (t1, t2,...,tn). 2

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Stochastic Processes With Applications To Finance

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