Discrete probability distributions.md (800B)
1 +++ 2 title = 'Discrete probability distributions' 3 template = 'page-math.html' 4 +++ 5 6 # Discrete probability distributions 7 8 experiment: possible outcomes, probability of outcome 9 random variable: possible values, probability of value 10 Tables, e.g. for dice: 11 12 <table> 13 <tr><th>x</th><th>P(X = x)</th></tr> 14 <tr><td>1</td><td>$\frac{1}{6}$</td></tr> 15 <tr><td>2</td><td>$\frac{1}{6}$</td></tr> 16 <tr><td>3</td><td>$\frac{1}{6}$</td></tr> 17 <tr><td>4</td><td>$\frac{1}{6}$</td></tr> 18 <tr><td>5</td><td>$\frac{1}{6}$</td></tr> 19 <tr><td>6</td><td>$\frac{1}{6}$</td></tr> 20 </table> 21 22 E(X): sum of (x times its probability) 23 24 $Var(X) = \sum_{i}^{k} \lbrack x_{i}^{2} P(X = x_{i}) \rbrack - \mu^{2}$ 25 26 in english: to get variance, sum the (square of each value times its probability) and subtract the square of the mean.