1. Show that the sum of two independent Gaussian random variables is itself a Gaussian random variable. What is the mean and variance?
Let and be two independent Gaussian random variables. with mean and and variance and
Similarly for .
Since the sum of two independent random variable X and Y is the product of the two seperate characteristic function.
The new random variable has mean and variance .
2. Calculate the characteristic function of the Exponential distribution.
Food for Thought Problems
Group : Noah, Kai, Tameen, Jin, Trettels