Bernoulli random variables almost surely random variable probability Bernoulli random variables
For example, if 




Y

1


,

Y

2


,
.
.
.



{\displaystyle Y_{1},Y_{2},...\,}

 are independent Bernoulli random variables taking values 1 with probability p and 0 with probability 1-p, then 





E


(

Y

i


)
=
p


{\displaystyle {\textrm {E}}(Y_{i})=p}

 for all i, so that 







Y
¯




n




{\displaystyle {\bar {Y}}_{n}}

 converges to p almost surely.
