Geometric Random Variable

Question

I'm reading about Geometric Random variables from a book, which is as follows:

$X_1, X_2,\ldots$ are independent identically distributed variables which are $\mathrm{Ber}(p)$

$$ Y = \min \{n\geq 1\mid X_n = 1\} \sim \mathrm{Geo}(p)$$

$$ Y \in\mathbb N$$

$$ P(Y=k) = p(1-p)^{k-1}$$

I am unsure why it goes on to say this: $E(Y) = \sum\limits_{k=1}^\infty kP(Y=k)$

Thanks

Answer 1

For any discrete random variable $X$, the expected value is $$ \mathbb E(X)=\sum_x x\Pr(X=x). $$