Characteristic function of z (Joint?)

[Grobo]

I need some help. Is there a good way to do this type of question?

Homework Statement

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

Homework Equations

N/A

 

[Ray Vickson]

I need some help. Is there a good way to do this type of question?

Homework Statement

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

Homework Equations

N/A

Yes, a good way to do this type of question is to use the results in your course notes and/or textbook, and to just go ahead and use the formulas. If you show your work and if you get stuck on some specific point, then come back and ask for advice.

RGV

 

[Grobo]

Well, by textbook ( or teachers .pdf ) does not explain how to do this kind of problem. I also found it difficult to find something about in on the internett that i understood.(Yes math is not one of my strongest subjects).

How should i begin to solve this problem?