Binomial Distribution

library(dplyr)
library(ggplot2)

e.random <-  rbinom(n = 10000, size = 10, prob = 0.5)

e.prop <- prop.table(table(e.random))
e.prop <- data.frame(e.prop)

t.prop = dbinom(x = 0:10, size = 10, prob = 0.5)
t.prop <- data.frame(x = 0:10, t.prop)

dat <- e.prop %>% 
  rename(
    x = e.random,
    e.prop = Freq
  ) %>% 
  mutate(
    x = as.numeric(x) - 1
  ) %>% 
  right_join(t.prop)

Joining, by = "x"

dat$e.prop.sum <- cumsum(dat$e.prop)
dat$t.prop.sum <- cumsum(dat$t.prop)

Yêu cầu 1

barplot(
  prop.table(
    table(e.random)
  )
)

Yêu cầu 2

ggplot(dat, aes(x)) +
  geom_line(aes(y = e.prop.sum, col = "ECDF")) + 
  geom_line(aes(y = t.prop.sum, col = "TCDF")) + 
  labs(
    title = "ECDF vs. TCDF",
    col = element_blank(), 
    y = "F(x)"
  ) + 
  theme_bw()