Computing the PDF f(z)

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Q: X~exponential r.v with parameter 1 (amount of time that takes for abuse to arrive)

Y~ Uniform distributed on [0,2].(time to load)

.X and Y are independent.

.Compute the pdf of the time for the bus to arrive plus the time to load.

. Then we are trying to find Z(x,y)=x+y

. In my picture, I have attached the work I have so far but I am just confused because I feel like my bounds are wrong, any feedback would be appreciated

enter image description here