The sum of random variables should not be confused with the sum of their distributions. If both distributions are normal, the former is also a normal distribution with appropriately scaled parameters. The latter would be what is called a Gaussian mixture. This piece will illustrate both sums, beginning with two normal distributions with identical standard deviations yet different means. First, we load necessary packages and define our distributions: pacman::p_load("ggplot2", "RColorBrewer", "extrafont") set.