# Math Help - about bernoulli

1. ## about bernoulli

Let Z1,Z2,Z3,...Zi be iid bernoulli random variables. Let Y be the first Zi to be 1. Calculate E(Y). I know it's a geometric distribution, then i write, E(Y)=∑ 1 x p x q^(y-1). Z1, Z2 Z3... Zi is a bernoulli distribution, so I think the value of Y to be the fisrt success is "1". however, i just wondering the value of Y is the value of Z1, Z2, Z3... ( 0, 1) or the number of trials to get the first success.. I need an explanation. Thx a lot..

2. Originally Posted by solskjaer
Let Z1,Z2,Z3,...Zi be iid bernoulli random variables. Let Y be the first Zi to be 1. Calculate E(Y). I know it's a geometric distribution, then i write, E(Y)=∑ 1 x p x q^(y-1). Z1, Z2 Z3... Zi is a bernoulli distribution, so I think the value of Y to be the fisrt success is "1". however, i just wondering the value of Y is the value of Z1, Z2, Z3... ( 0, 1) or the number of trials to get the first success.. I need an explanation. Thx a lot..
More properly, $Y$ is the first $i$ such that $Z_i=1$. Thus it is an integer greater that or equal to 1. As a consequence, $E[Y]=\sum_{y=1}^\infty y pq^{y-1}=\cdots=\frac{1}{p}$.