Exercise2.71mentionedthatwhen Y has positivelyskeweddistributionoverthepositivereal line, statisticalanalysesoftentreat log(Y ) as havinga N(, 2) distribution. Then Y has the

Exercise2.71mentionedthatwhen Y has positivelyskeweddistributionoverthepositivereal line, statisticalanalysesoftentreat log(Y ) as havinga N(μ, σ2) distribution. Then Y has the log-normaldistribution, whichhas pdf for y > 0, f(y; μ, σ) = [1~y(

º

2πσ)] exp{−[log(y) − μ]2~2σ2}.

(a) For n independentobservations {yi}, findtheMLestimatesof μ and σ2.

(b) FindtheestimatedstandarderrorfortheMLestimator ˆμ.

(c) UsingtheinvariancepropertyofMLestimators,findtheMLestimatesofthemeanand varianceofthedistribution,whichare E(Y ) = eμ+σ2~2 and var(Y ) = (eσ2 − 1)[E(Y )]2.