Question

Question about using the convolution of distribution:

1. we have the formula: integral fx(x)fy(z-x)dx=integral fx(z-x)fy(x)dx

I know this are equivalent. However, how do I decide which side I should use ?

For example,X~Exp(1) and Y~Unif [0,1] X and Y independnt and the textbook use fx(z-x)fy(x)dx.

However, can I use the left hand side fx(x)fy(z-x)dx???is there any constraint for using left or right or actually both can lead me to the right answer???

2. For X and Y are independent and exponential distribution, however, why all the text book just ignore the infinity?

they use integral from 0 to z fx(x)*fy(z-x) to find the distribution X+Y, however, in my understand exponential distribution should be from 0 to infinity

Answer 1