information:classification
Coin toss

The possible outcomes for one coin toss can be described by the sample space Ω = { heads, tails } {\displaystyle \Omega =\{{\text{heads}},{\text{tails}}\}}. We can introduce a real-valued random variable Y {\displaystyle Y} that models a $1 payoff for a successful bet on heads as follows: Y (ω) = { 1, if ω = heads, 0, if ω = tails. {\displaystyle Y(\omega)={\begin{cases}1,&{\text{if }}\omega ={\text{heads}},\\0,&{\text{if }}\omega ={\text{tails}}.\end{cases}}}

If the coin is a fair coin, Y has a probability mass function f Y {\displaystyle f_{Y}} given by: f Y (y) = { 1 2, if y = 1, 1 2, if y = 0, {\displaystyle f_{Y}(y)={\begin{cases}{\tfrac {1}{2}},&{\text{if }}y=1,\\{\tfrac {1}{2}},&{\text{if }}y=0,\end{cases}}}