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1. The problem statement, all variables and given/known data

Let X and Y be independent random Variables with exponential densities

fX(x) = Ωe^{-Ωx}, if X≥0

0, otherwise

fY(y) = βe^{-βy}, if y≥0

0, otherwise

Respectively, where η and β are positive real-valued constants.

1) Find the characteristic function ∅z of Z = X+Y

2) Find the probability density function fZ(z) of Z = X+Y

2. Relevant equations

N/A

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# Characteristic function of z (Joint?)

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