8. Let X1,..., X, be a random sample from a population that only takes positive values. Use the central limit theorem to show that, for large n, the product Y = X1X2·… X, and the geometric mean G = VY have approximately lognormal distributions. What are the parameters of these distributions, in terms of the population parameters?

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8.
Let X1,..., X, be a random sample from a population that only takes positive values.
Use the central limit theorem to show that, for large n, the product Y = X1X2· X, and
the geometric mean G
parameters of these distributions, in terms of the population parameters?
VY have approximately lognormal distributions. What are the
Transcribed Image Text:8. Let X1,..., X, be a random sample from a population that only takes positive values. Use the central limit theorem to show that, for large n, the product Y = X1X2· X, and the geometric mean G parameters of these distributions, in terms of the population parameters? VY have approximately lognormal distributions. What are the
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