Poisson density curve, histogram and shaded area with ggplot2?

Question

How to make:

1. a density curve and histogram displaying a poisson distribution with lambda = 2.5; and
2. a density curve with shaded area showing P(X >= 4 with lambda = 2.5)

the x axis should be 0 to 10

Answer 1

Poisson distribution is a discrete probability distribution (function is defined only at integer values). So instead of a line it is better represented with points at integer values. To color a specific range under a function one can use geom = "area" and xlim = c(min(range), max(range):

ggplot(data.frame(x = 0:10), aes(x)) +
  stat_function(geom = "point", n = 11, fun = dpois, args = list(lambda = 2.5)) +
  stat_function(geom = "area", aes(x), n = 7, fun = dpois, args = list(lambda = 2.5), xlim = c(4,10), fill = "lightblue", alpha = 0.5)+
  theme_bw()+
  scale_x_continuous(breaks = 0:10)

If the n argument in stat_function does not match the number of integer values over a range the plot is going to look funky.