Sum of gaussian random variables

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If X1 is a lognormal random variable with parameters (α, β1 ), and X2 is a lognormal random variable with parameters (α, β2 ), it has been postulated that the product: Y = X1 X2 has a lognormal distribution with parameters (α, βy ) where: βy = β1 + β2

(i) Con?rm this result theoretically. (Hint : use results from Chapter 6 regarding the sum of Gaussian random variables.)

(ii) In the data table below, X1 is a random sample drawn from a distribution pur- ported to be L(0.25, 0.50); and X2 is a random sample drawn from a distribution purported to be L(0.25, 0.25).

X1 1.16741	X2 1.61889
1.58631	1.15897
2.00530	1.17163
1.67186	1.09065
1.63146	1.27686
1.61738	0.91838
0.74154	1.45123
2.96673	1.47800
1.50267	2.16068
1.99272	1.46116

From this data set, obtain the corresponding values for Y de?ned as the product Y = X1 X2 . According to the result stated and proved in (i), what is the theoretical distribution of Y ? Con?rm that the computed sample data set for Y agrees with this postulate.

Reference no: EM131002791

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