# Eleisha's Segment 9: Characteristic Functions

To Calculate:

1. Use characteristic functions to show that the sum of two independent Gaussian random variables is itself a Gaussian random variable. What is its mean and variance?

2. Calculate (don't just look up) the characteristic function of the Exponential distribution.

$\displaystyle \phi_X(t) = \int_0^\infty e^{itx} \cdot \lambda e^{\lambda x} dx$

$\displaystyle \phi_X(t) = \lambda \int_0^\infty e^{itx} e^{-(\lambda - it)x} dx$