# Coin Flipping

A Bernoulli process is a repeated coin flipping, possibly with an unfair coin (but with consistent unfairness).

## 3 - Random Variable

$$Y(\omega) = \begin{cases} 1, & \text{if } \omega = \text{heads}, \\[6pt] 0, & \text{if } \omega = \text{tails}. \end{cases}$$

## 4 - Sample space

$$\Omega = \{ \text{heads} , \text{tails} \}$$

## 5 - PMF

If the coin is a fair coin, Y has a probability mass function given by:

$$f_Y(y) = \begin{cases} \frac 12,& \text{if }y=1,\\[6pt] \frac 12,& \text{if }y=0, \end{cases}$$