Question

Let ๐‘‹ and ๐‘Œ be independently random variables, with ๐‘‹ uniformly distributed on [0,1] and ๐‘Œ uniformly distributed on [0,2] . Find the PDF ๐‘“๐‘(๐‘ง) of ๐‘=max{๐‘‹,๐‘Œ} .

For ๐‘ง<0 or ๐‘ง>2 :

๐‘“๐‘(๐‘ง)=

For 0โ‰ค๐‘งโ‰ค1 :

๐‘“๐‘(๐‘ง)=

For 1โ‰ค๐‘งโ‰ค2 :

๐‘“๐‘(๐‘ง)=

I think for the first scenario is the PDF is 0 since the bounds are outside of the range.

if anybody got hint for the other two, thanks

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