Let X have an exponential distribution with 1 (a) Find the first four cumulants of the distribution of X (b) Use the expressions in Section 8 4 to calculate the third and fourth moments of Zn p n Xn for n 10, n 100, n 1000 (c) How large does n be in order to for the third and fourth moments to be close to those of the normal approximation (Use your judgment to assess closeness )

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Question: Let X have an exponential distribution with 1. (a) Find the first four cumulants of the distribution of X. (b) Use the expressions

Let X have an exponential distribution with ¸ Æ 1.

(a) Find the first four cumulants of the distribution of X.

(b) Use the expressions in Section 8.4 to calculate the third and fourth moments of Zn Æ

p n

Xn ¡¹

for n Æ 10, n Æ 100, n Æ 1000.

(c) How large does n be in order to for the third and fourth moments to be “close” to those of the normal approximation. (Use your judgment to assess closeness.)

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