1. ## Flipping coins

I'm trying to write out the following Bernoulli Space events in terms of $\displaystyle E_n$

$\displaystyle \Omega = \{ \omega = \omega_1 \omega_2 \omega_3 \ldots : \omega_n = 1,0 \}$

(i) exactly 2 heads are obtained.

$\displaystyle E_x=\{ \omega \in \Omega : \omega_x=1 \}$

$\displaystyle E_y=\{ \omega \in \Omega : \omega_y=1 \}$

$\displaystyle E_z= \{\omega \in \Omega : \omega_z=0 \}$

then:

$\displaystyle \left( \bigcap_{z=1}^{\infty}E_z \right) \setminus (E_x \cap E_y )$

$\displaystyle E_n=\{ \omega \in \Omega : \omega_n \omega_{n+1} \omega_{n+2} \ne 010 \}$

then:

$\displaystyle \bigcap_{n=1}^{\infty}E_n$

Look good?

2. ## Re: Flipping coins

or for the first one would this be correct?

$\displaystyle \left( \bigcap_{z=1}^{\infty}E_z \right) \cap E_x \cap E_y$