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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 |
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- $X$ 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. | ||

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+ | Answers: | ||

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+ | - $p_X(x) = \begin{cases}\frac{3}{5},& \text{if } x = 2, \\ \frac{2}{5},& \text{if } x = 3, \\ 0,& \text{otherwise}.\end{cases}$ | ||

+ | - $p_X(x) = \begin{cases}\frac{1}{16},& \text{if } x = 0, \\ \frac{1}{4},& \text{if } x = 1, \\ \frac{3}{8},& \text{if } x = 2, \\ \frac{1}{4},& \text{if } x = 3, \\ \frac{1}{16},& \text{if } x = 4, \\ 0,& \text{otherwise}. \end{cases}$ | ||

+ | - $p_Y(y) = \begin{cases}\frac{188}{221},& \text{if } y = 0, \\ \frac{32}{221},& \text{if } y = 1, \\ \frac{1}{221},& \text{if } y = 2, \\ 0,& \text{otherwise}.\end{cases}$ | ||

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