# Differences

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 math-340:m340-f15-hw:hw-9 [2015/09/15 06:33]dcs created math-340:m340-f15-hw:hw-9 [2015/09/20 09:34] (current)dcs 2015/09/20 09:34 dcs 2015/09/15 06:33 dcs created 2015/09/20 09:34 dcs 2015/09/15 06:33 dcs created Line 12: Line 12: - $X$ is the number of heads in four tosses of a fair coin. - $X$ is the number of heads in four tosses of a fair coin. - $Y$ is number of aces when two cards are drawn a random from a standard deck of 52 cards. - $Y$ is number of aces when two cards are drawn a random from a standard deck of 52 cards. + + Answers: + + - $p_X(x) = \begin{cases}\frac{3}{5},&​ \text{if } x = 2, \\ \frac{2}{5},&​ \text{if } x = 3, \\ 0,& \text{otherwise}.\end{cases}$ + - $p_X(x) = \begin{cases}\frac{1}{16},&​ \text{if } x = 0, \\ \frac{1}{4},&​ \text{if } x = 1, \\ \frac{3}{8},&​ \text{if } x = 2, \\ \frac{1}{4},&​ \text{if } x = 3, \\ \frac{1}{16},&​ \text{if } x = 4, \\ 0,& \text{otherwise}. \end{cases}$ + - $p_Y(y) = \begin{cases}\frac{188}{221},&​ \text{if } y = 0, \\ \frac{32}{221},&​ \text{if } y = 1, \\ \frac{1}{221},&​ \text{if } y = 2, \\ 0,& \text{otherwise}.\end{cases}$ +