Question

Consider x and y independent Gaussian random variables with zero mean and unity variance. What is the probability density function (PDF) of the sum of x and y?

1) Normal distribution
2) Uniform distribution
3) Exponential distribution
4) Chi-squared distribution

Answer 1

The PDF of the sum of two independent Gaussian random variables with zero mean and unity variance is a normal distribution (option 1).

Step-by-step explanation:

The sum of two independent Gaussian random variables with zero mean and unity variance is also a Gaussian random variable. Therefore, the PDF of the sum of x and y is a normal distribution (option 1).