# Math Help - Pdf of minimum of (x,c)

1. ## 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

2. To be sure, I tried solving it myself, and I get a different result.

Check it on:

3. 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.