Normal Distribution Exercise

[ahahs]

Let W = e x where X ∼ N(µ, σ2 ). Find cumulative distribution function and probability density function of W. (CDF should be defined by using standard normal φ)

 

[HallsofIvy]

Do you mean \(\displaystyle W= e^x\) (W= e^x)?

 

[ahahs]

Do you mean \(\displaystyle W= e^x\) (W= e^x)?

Yes

 

[Romsek]

This is pretty straightforward.

[MATH]F_W(w) = P[W<w] = P[e^X < w] = P[X < \ln(w)][/MATH]
and this is simple since you have the CDF of [MATH]X[/MATH]
[MATH]f_W(w) = \dfrac{d}{dw} F_W(w)[/MATH]
You'll also need to specify what the range of [MATH]W[/MATH] is as well.