Communication, Networking, Signal and Image Processing (CS)
Question 1: Probability and Random Processes
August 2015
Let $ \lambda = \frac{1}{\mu} $, then $ E(X)=E(Y)=\frac{1}{\lambda} $.
$ \phi_{X+Y}=E[e^{it(X+Y)}]=\int_{X}\int_{Y}e^{it(X+Y)}p(x,y)dxdy $
As X and Y are independent
$ \phi_{X+Y}=\int_{x}\int_{y}e^{it(x+y)}p(x)p(y)dxdy = \int_{X}e^{itx}p(x)\int_{Y}e^{ity}p(y)dxdy $
