Defining Joint Probability Distributions

Fully independent: Variables x₁ through x_k, $\Pr(x_1)$ through $\Pr(x_k)$.

$\Pr(TFTTFTFT)$

• $= \Pr(x_1)\Pr(\overline{x_2}\vert x_1)\Pr(x_3\vert\overline{x_2}x_1)\Pr(x_4\vert x_3\overline{x_2}x_1)\ldots$
• $= \Pr(x_1)(1-\Pr(x_2))\Pr(x_3)\Pr(x_4)(1-\Pr(x_5))\ldots$