Properties of Bernoulli random variables

• Theorem: Let $X \sim Bernoulli(p)$, then:
  • $\mathbb{E}[X] = p$
  • $\mathbb{E}[X^2] = p$
  • $Var[X] = p\cdot (1-p)$

states <- c(0, 1)
p <- 0.3

plot(
  states, dbinom(states, 1, p), type = 'h',
  ylim = c(0, 1), main = "Bernoulli(p)",
  xlab = "States", ylab = "Probabilities"
)