DES - Demonstration on How to Use the Superposition

Arguments

• DES - Exponential Distribution

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Given:

We have that:

Being both exponential distribution ($0$ for $t\ge 0$) and $t\ge 0$ we only care about the first quadrant.

Also we know that: $X$, $Y$ are independent, so:

Which brings as to the demonstration:

It can also be written as:

And for $t=0$ we get: