Coin Flipping

About

discrete random_variable

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

Random Variable

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

Sample space

<MATH> \Omega = \{ \text{heads} , \text{tails} \} </MATH>

PMF

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

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

Documentation / Reference


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