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Chapter 5: Q 5.39 (page 214)

If Xis an exponential random variable with a parameter位=1, compute the probability density function of the random variable Ydefined by Y=logX

Short Answer

Expert verified

Therefore, the probability density function of the random variableY=ey脳e-ey

Step by step solution

01

Given information:

If X is an exponential random variable with parameter位=1,

02

Explanation:

Fx(x)=1-e-x

So if

Y=lnx

We have

FY(y)=P(Y鈮�y)=P(lnX鈮�y)=P(X鈮�ey)=FXey=1-e-ey

03

Explanation:

Therefore, the probability density function of the random variable is

fY(y)=ddy1-e-ey=--eye-ey=ey脳e-ey

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