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Suppose that we have a random sample X1, · · , Xn drawn from a distribution...

Suppose that we have a random sample X1, · · , Xn drawn from a distribution that only takes positive values. Suppose that the sample size n is sufficiently large. Consider the new random variable ∏ n i=1 Xi . Derive the distribution of this new random variable and explain your reasoning mathematically

Math   Statistics-And-Probability   
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Answer #1

Let Z =

Let the probability distribution of be f(x), i = 1,2,...n.

Now, the distribution of Z is, f(Z) = f() = f() = f()f()....f() [As, , ,... are random sample, they are independent] = .

[As , ,...., are identical]

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