Problem 3. Consider a random sample X1, X2,..., Xn from a distribution with log-normal pdf (density...

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Problem 3. Consider a random sample X1, X2,..., Xn from a distribution with log-normal pdf (density function): for t 0 and 0 otherwise. Both μ and σ 0 are unknown parameters. Find the method of moments estinates μ and σ. Hint: computing moments, change of variable y = Int might be useful.

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Answer 1

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Sol wion we know that If X cu LN C4,02) then Fx (2) = 1 :-!. (In-ce )? X ROSTEės josxso -OLM200 60 ; otherwise and c ut 62) E . by subtracting o from @ we get 24+262 = In (Vcx)) - 2M +_62 = 2 In (E(x)) 62 = 1n cx(x)) - 2 In E (x)) - 0 ŽIEC put value o

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