MAS_209_NOTE_pages_5.pdf_pages_11.pdf.pdf

Distribution of Functions of Random Variables – CDF Technique




Step 4: Final Piecewise CDF

0 2
 if w ≤ 0,
w

if 0 < w < 1,
FW (w) = 2
2


 −w /2 + w if 1 ≤ w < 2,
1 if w ≥ 2.


Step 5: Differentiate to Get the PDF
We now differentiate FW (w) to obtain the PDF:


 0 w ≤ 0,

d  w 0 < w < 1,
fW (w) = FW (w) =
dw 
 1−w 1 ≤ w < 2,

0 w ≥ 2.





Sam Maseno University August 19, 2025



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