vec1 = c("foo", "bar")

vec2 = c(31, 42)

vec3 = c(1, 2)

df = data.frame(name = vec1, ages = vec2, salary = vec3)

df

names(df) = c("last.name", "age", "annual.income")

df

x = list(a = c(1, 2), b = c(3, 4), c = c(5, 6))

x

stack(x)

x_grid = seq(-8, 8, length.out = 100)

gaussian_function =

function(x, s) exp(-x ^ 2 / (2 * s ^ 2)) / (sqrt(2 * pi) * s)

df = stack(list("$\\sigma = 1$" = gaussian_function(x_grid, 1),

"$\\sigma = 2$" = gaussian_function(x_grid, 2),

"$\\sigma = 3$" = gaussian_function(x_grid, 3),

"$\\sigma = 4$" = gaussian_function(x_grid, 4)))

names(df) = c("y", "sigma");

df$x = x_grid

head(df)

qplot(x,

y,

color = sigma,

lty = sigma,

geom = "line",

data = df,

main = "Normal Density for Different $\\sigma$ Values",

xlab = "$x$",

ylab = "$f(x)$")