1. The problem statement, all variables and given/known data A random variable x has a probability density function given by fX(x) = e-x , x ≥ 0 and an independent random variable Y has a probability density function of fY(y) = ey , y ≤ 0 using the characterisic functions, find the probability density function of Z = X + Y 2. Relevant equations [itex]\Phi[/itex]X([itex]\omega[/itex]) = E[ejωx] = ∫fX(x)ejωxdx [itex]\Phi[/itex]Z(ω) = [itex]\Phi[/itex]X([itex]\omega[/itex]) * [itex]\Phi[/itex]Y([itex]\omega[/itex]) fZ(z) = 1/ (2[itex]\pi[/itex]) ∫ [itex]\Phi[/itex]Z(ω) * e-jωz the integrals within section 2 are from negative infinity to positive infinity . . . also it's 1 over 2 pi . . didn't know how to make that into a fraction 3. The attempt at a solution My attempt was scanned and uploaded via photobucket.. here's the scan! http://i359.photobucket.com/albums/oo39/r19ecua/scan0356.jpg I'm wondering if Cauchy's was a good way to handle this..