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math-340:m340-f15-hw:hw-1 [2015/08/26 05:51] – dcs | math-340:m340-f15-hw:hw-1 [2015/08/31 05:41] (current) – dcs | ||
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- $\cup_{k=1}^\infty E_k$ | - $\cup_{k=1}^\infty E_k$ | ||
- $\cap_{k=1}^\infty E_k$ | - $\cap_{k=1}^\infty E_k$ | ||
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+ | Answers: | ||
+ | |||
+ | 1. a. $\Omega = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}$ | ||
+ | |||
+ | b. $E = \{HHH, HHT, HTH, THH, HTT, THT, TTH\}$ | ||
+ | |||
+ | 2. a. $\Omega = [0, \infty)$ | ||
+ | |||
+ | b. I. $E_1 \cup E_2 \cup E_3 = [0, 3)$ | ||
+ | |||
+ | II. $E_1 \cap E_2 \cap E_3 = [0, 1)$ | ||
+ | |||
+ | III. $E_3 \cap E_2^c = [2, 3)$ | ||
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+ | IV. $\cup_{k=1}^\infty E_k = \Omega = [0, \infty)$ | ||
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+ | V. $\cap_{k=1}^\infty E_k = [0, 1)$ |