| Both sides previous revisionPrevious revision | |
| math-340:m340-f15-hw:hw-12 [2015/10/08 18:32] – dcs | math-340:m340-f15-hw:hw-12 [2015/10/11 09:03] (current) – dcs |
|---|
| - $p_Z(z) = \begin{cases}\frac{1}{7},& \text{if } z = 0, \\ \frac{2}{7},& \text{if } z = 1, \\ \frac{2}{7},& \text{if } z = 4, \\ \frac{2}{7},& \text{if } z = 9, \\ 0,& \text{otherwise}.\end{cases}$ | - $p_Z(z) = \begin{cases}\frac{1}{7},& \text{if } z = 0, \\ \frac{2}{7},& \text{if } z = 1, \\ \frac{2}{7},& \text{if } z = 4, \\ \frac{2}{7},& \text{if } z = 9, \\ 0,& \text{otherwise}.\end{cases}$ |
| - $p_T(t) = \begin{cases}\frac{1}{25},& \text{if } t = -4, 4, \\ \frac{2}{25},& \text{if } t = -3, 3, \\ \frac{3}{25},& \text{if } t = -2, 2, \\ \frac{4}{25},& \text{if } t = -1, 1, \\ \frac{1}{5},& \text{if } t = 0, \\ 0,& \text{otherwise}.\end{cases}$ | - $p_T(t) = \begin{cases}\frac{1}{25},& \text{if } t = -4, 4, \\ \frac{2}{25},& \text{if } t = -3, 3, \\ \frac{3}{25},& \text{if } t = -2, 2, \\ \frac{4}{25},& \text{if } t = -1, 1, \\ \frac{1}{5},& \text{if } t = 0, \\ 0,& \text{otherwise}.\end{cases}$ |
| - | - $p_S(s) = \begin{cases}\frac{1}{25},& \text{if } s = -4, 4, \\ \frac{2}{25},& \text{if } s = -3, 3, \\ \frac{3}{25},& \text{if } s = -2, 2, \\ \frac{4}{25},& \text{if } s = -1, 1, \\ \frac{1}{5},& \text{if } s = 0, \\ 0,& \text{otherwise}.\end{cases}$ |
| - | - $p_Z(z) = \begin{cases}\frac{2}{5},& \text{if } z = 0, \\ \frac{2}{5},& \text{if } z = 2, \\ \frac{1}{5},& \text{if } x = 6, \\ 0,& \text{otherwise}.\end{cases}$ |
| - $p_W(w) = \begin{cases}\frac{1}{100},& \text{if } w = 1, \\ \frac{3}{100},& \text{if } w = 2, \\ \frac{1}{20},& \text{if } w = 3, \\ \frac{7}{100},& \text{if } w = 4, \\ \frac{9}{100},& \text{if } w = 5,\\ \frac{11}{100},& \text{if } w = 6, \\ \frac{13}{100},& \text{if } w = 7, \\ \frac{3}{20},& \text{if } w = 8, \\ \frac{17}{100},& \text{if } w = 9, \\ \frac{19}{100},& \text{if } w = 10, \\ 0,& \text{otherwise}.\end{cases}$ $p_U(u) = \begin{cases}\frac{19}{100},& \text{if } w = 1, \\ \frac{17}{100},& \text{if } w = 2, \\ \frac{3}{20},& \text{if } w = 3, \\ \frac{13}{100},& \text{if } w = 4, \\ \frac{11}{100},& \text{if } w = 5,\\ \frac{9}{100},& \text{if } w = 6, \\ \frac{7}{100},& \text{if } w = 7, \\ \frac{1}{20},& \text{if } w = 8, \\ \frac{3}{100},& \text{if } w = 9, \\ \frac{1}{100},& \text{if } w = 10, \\ 0,& \text{otherwise}.\end{cases}$ | - $p_W(w) = \begin{cases}\frac{1}{100},& \text{if } w = 1, \\ \frac{3}{100},& \text{if } w = 2, \\ \frac{1}{20},& \text{if } w = 3, \\ \frac{7}{100},& \text{if } w = 4, \\ \frac{9}{100},& \text{if } w = 5,\\ \frac{11}{100},& \text{if } w = 6, \\ \frac{13}{100},& \text{if } w = 7, \\ \frac{3}{20},& \text{if } w = 8, \\ \frac{17}{100},& \text{if } w = 9, \\ \frac{19}{100},& \text{if } w = 10, \\ 0,& \text{otherwise}.\end{cases}$ $p_U(u) = \begin{cases}\frac{19}{100},& \text{if } w = 1, \\ \frac{17}{100},& \text{if } w = 2, \\ \frac{3}{20},& \text{if } w = 3, \\ \frac{13}{100},& \text{if } w = 4, \\ \frac{11}{100},& \text{if } w = 5,\\ \frac{9}{100},& \text{if } w = 6, \\ \frac{7}{100},& \text{if } w = 7, \\ \frac{1}{20},& \text{if } w = 8, \\ \frac{3}{100},& \text{if } w = 9, \\ \frac{1}{100},& \text{if } w = 10, \\ 0,& \text{otherwise}.\end{cases}$ |
| | - $P(U < W) = \frac{9}{10}$, $P(U \le W) = 1$; $U$ and $W$ are not independent: for example, $P(U = 10, W = 1) = 0 \ne p_U(10)p_W(1)$ |
