Find the probability density function of Y=e^{X}



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Find the probability density function of Y=eX, when X is normally distributed with parameters μ and σ2. The random variable Y is said to have a lognormal distribution (since log Y has a normal distribution) with parameters μ and σ2

Answer & Explanation



Skilled2021-02-02Added 109 answers

XN(μ, σ2) and YeX.

Observe that Y>0 with porbability 1.

For ant y>0 FY(y)=P(Yy)=P(exy)=P(Xlog(y))=FX(log(y))

fY(y)=d dy Fy(y)=fX(log(y))1y=1σ2πexp((loguμ)22σ2)1y

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