Hi, I'm studying for an exam and I'm studying this problem:

Let $\displaystyle X_1, X_2,...,X_n $ be i.i.d. to $\displaystyle N( \mu , 1) $ with $\displaystyle \mu $ unknown.

And suppose that $\displaystyle Y_i = I(X_i<0) \ \ \ \ \forall i = 1,...,n $

The solution says that then $\displaystyle Y_i = Bernulli(p) $ where $\displaystyle p=Pr(X<0)= \Phi (- \mu ) $ where $\displaystyle \Phi ( \dot )$ is the standard nomral cdf.

But I don't understand the last part when the distribution can be written as the standard nomral cdf.

Please help, thanks!!!