This shows you the differences between two versions of the page.
Next revision | Previous revision | ||
math-340:m340-f15-hw:hw-1 [2015/08/25 08:02] – created dcs | math-340:m340-f15-hw:hw-1 [2015/08/31 05:41] (current) – dcs | ||
---|---|---|---|
Line 8: | Line 8: | ||
- Suppose a fuse is tested until it fails. | - Suppose a fuse is tested until it fails. | ||
- Find a sample space for this experiment. | - Find a sample space for this experiment. | ||
- | - Let $E_k$ be the event that a fuse fails in less than $k$ hours, $k = 1, 2, \ldots$. Find $E_1 \cup E_2 \cup E_3$, $E_1 \cap E_2 \cap E_3$ $\cup_{k=1}^\infty E_k$, and $\cap_{k=1}^\infty E_k$ | + | - Let $E_k$ be the event that a fuse fails in less than $k$ hours, $k = 1, 2, \ldots$. Find |
+ | - $E_1 \cup E_2 \cup E_3$ | ||
+ | - $E_1 \cap E_2 \cap E_3$ | ||
+ | - $E_3 \cap E_2^c$ | ||
+ | - $\cup_{k=1}^\infty E_k$ | ||
+ | - $\cap_{k=1}^\infty E_k$ | ||
+ | |||
+ | |||
+ | 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. $E_3 \cap E_2^c = [2, 3)$ | ||
+ | |||
+ | IV. $\cup_{k=1}^\infty E_k = \Omega = [0, \infty)$ | ||
+ | |||
+ | V. $\cap_{k=1}^\infty E_k = [0, 1)$ |