Editing Joint probability distribution (section)

===Coin flips===
Consider the flip of two [[fair coin]]s; let <math>A</math> and <math>B</math> be discrete random variables associated with the outcomes of the first and second coin flips respectively. Each coin flip is a [[Bernoulli trial]] and has a [[Bernoulli distribution]]. If a coin displays "heads" then the associated random variable takes the value 1, and it takes the value 0 otherwise. The probability of each of these outcomes is {{sfrac|1|2}}, so the marginal (unconditional) density functions are

:<math>P(A)=1/2 \quad \text{for} \quad A\in \{0, 1\};</math>
:<math>P(B)=1/2 \quad \text{for} \quad B\in \{0, 1\}.</math>

The joint probability mass function of <math>A</math> and <math>B</math> defines probabilities for each pair of outcomes. All possible outcomes are
:<math>
(A=0,B=0),
(A=0,B=1),
(A=1,B=0),
(A=1,B=1).
</math>
Since each outcome is equally likely the joint probability mass function becomes
:<math>P(A,B)=1/4 \quad \text{for} \quad A,B\in\{0,1\}.</math>

Since the coin flips are independent, the joint probability mass function is the product
of the marginals:
:<math>P(A,B)=P(A)P(B) \quad \text{for} \quad A,B \in\{0,1\}.</math>