# Pdf of minimum of (x,c)

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• May 12th 2011, 09:05 PM
rpmatlab
Pdf of minimum of (x,c)
I have to find the pdf of y = minimum of (x,c) where $X$ is a Random Variable with exponential distribution and ' $c$' is a constant. The detailed steps of my approach was given in the attachment. Is this approach correct? Please comment on the correctness of the solution
• May 13th 2011, 04:44 AM
rargh
To be sure, I tried solving it myself, and I get a different result.

Check it on:

https://docs.google.com/document/pub...tpnmGR2yr9Osn0
• May 13th 2011, 06:59 AM
theodds
Strictly speaking, Y doesn't admit a pdf. There is an atom at c: $P(c \le y) = 1$ or $0$ according as $c \le y$ or $c > y$ (note both are constants) so there is an error in this step in your work.

You can do this with the dirac delta function if you're comfortable with that. It looks like rargh has the right answer.