Bernoulli#
\[
I \sim \text{Bernoulli}(p)
\]
The Bernoulli probability distribution is
\[
P(I=k) = kp + (1-k)(1-p)
\]
more naturally,
\(I=k\) |
\(P(I=k)\) |
|---|---|
\(1\) |
\(p\) |
\(0\) |
\(1-p\) |
Expected Value : $\( \mathbb E[I] = p \)$
Variance : $\( \text{Var}[I] = pq \)$
Covariance : $\( \text{Cov}[I_1,I_2] = P(I_1=1, I_2=1) -P(I_1=1)P(I_2=1) \)$
MGF : $\( M_X(t) = pe^t + q \)$