Class notes Probability and Statistics II (2103)

Bernoulli distribution


Consider a single trial with two outcomes:
! success (1) or failure (0).
If the probability of success is p, then the pmf is

y 0 1
P(Y = y ) 1−p p

,Expected value and variance of Bernoulli

What is E[Y ] and Var(Y ) of a Bernoulli random va

,Bernoulli distribution

Bernoulli random variables arise frequently as indica
The indicator of an event A is the random variable

!
1, if A occurs,
1A =
0, if A does not occur.

Then 1A is a Bernoulli random variable with parame
the convenient property that

, Bernoulli in R

If


X ∼ Bernoulli(p)

! P(X = x ):
dbinom(x = x, size = 1, prob = p)

! P(X ≤ x )
pbinom(q = x, size = 1, prob = p)