A random variable Y is said to have a lognormal distribution if log Y has a normal
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(a) If X1, X2, . . . is an independent sequence of uniform (0, 1) variables, show that the product has an approximate lognormal distribution. Show that the mean and variance of log Y are, respectively, n and n.
(b) If Y = eX, with X ¼ Norm(μ, Ï2), it can be shown that
Let X1, . . . , X100 be an independent sequence of uniform (0,1) variables. Estimate
(c) Verify the aforementioned results with a simulation experiment in R.
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