Show that the characteristic function of X N , 2 Rm is for t 2 Rm Hint Startwithm 1 Establish E exp(i tZ) exp 1 2 t 2 by integration Then generalize to X N , for t 2 Rm using the same steps as in Exercises 5 11 and 5 12 C(t) E exp(it'X) exp(i't ...

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Show that the characteristic function of X N , 2 Rm is for t 2

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Show that the characteristic function of X »N

¹,§

2 Rm is

image text in transcribed

for t 2 Rm.
Hint: Startwithm Æ 1. Establish E £
exp(i tZ)
¤
Æ exp ¡
¡1 2 t 2¢
by integration. Then generalize to X »N ¡
¹,§
¢
for t 2 Rm using the same steps as in Exercises 5.11 and 5.12.

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Probability And Statistics For Economists

ISBN: 9780691235943

1st Edition

Authors: Bruce Hansen

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Question Posted: Sep 23, 2024 07:00 AM

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Show that the characteristic function of X N , 2 Rm is for t 2

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|C(t) =E[exp(it'X)] = exp(i't-

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Probability And Statistics For Economists

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