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Chapter 4: Q.4.2 (page 169)

If X has distribution function F, what is the distribution function of eX?

Short Answer

Expert verified

In the given information The distribution of eXcan be written as composition of logarithm function and distribution function of X

Step by step solution

01

Step 1:Given Information

Take any a鈭�suppeX(the support of eXis not specified since we are not given the support of X ).We have that

FeX(a)=PeX鈮�a=P(X鈮�log(a))=FX(loga)

02

Explanation

eXcan be written as composition of logarithm function and distribution function of X

03

Final Answer

The distribution of eXcan be written as composition of logarithm function and distribution function of X

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