EBook Problems MultivariateNormal
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===Problem 1=== | ===Problem 1=== | ||
| - | Person1 and Person2 are travelling from point A to point D, but there are different routes to get from A to D. Person1 decides to take the | + | Person1 and Person2 are travelling from point A to point D, but there are different routes to get from A to D. Person1 decides to take the A->B->D route, whereas Person2 takes the A->C->D route. |
[[Image:Problem_1.jpg|center]] | [[Image:Problem_1.jpg|center]] | ||
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| + | The travel times (in hours) between each pair of points indicated are normally distributed as follows: | ||
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| + | T1 ~ N (6, 2) | ||
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| + | T2 ~ N (4, 1) | ||
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| + | T3 ~ N (5, 3) | ||
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| + | T4 ~ N (4, 1) | ||
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| + | Explain why these times are stochastic (and not exact or deterministic)? Although the travel times here generally can be assumed statistically independent, T3 and T4 are dependent with correlation coefficient 0.8. | ||
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| + | ''(a) What is the probability that Person2 will not arrive at point D within 10 hours? (0.397) | ||
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| + | ''(b) 0.4 | ||
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| + | ''(c) Approximately 0.1587 | ||
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| + | ''(d) Approximately 0 | ||
| + | {{hidden|Answer for part (a)| | ||
| + | Let T2 be Person2’s travel time in (hours); T2 = T3 + T4 with | ||
| + | }} | ||
Revision as of 21:17, 6 January 2011
EBook Problems Set - Mutivariate Normal Distribution
Problem 1
Person1 and Person2 are travelling from point A to point D, but there are different routes to get from A to D. Person1 decides to take the A->B->D route, whereas Person2 takes the A->C->D route.
The travel times (in hours) between each pair of points indicated are normally distributed as follows:
T1 ~ N (6, 2)
T2 ~ N (4, 1)
T3 ~ N (5, 3)
T4 ~ N (4, 1)
Explain why these times are stochastic (and not exact or deterministic)? Although the travel times here generally can be assumed statistically independent, T3 and T4 are dependent with correlation coefficient 0.8.
(a) What is the probability that Person2 will not arrive at point D within 10 hours? (0.397)
(b) 0.4
(c) Approximately 0.1587
(d) Approximately 0
Answer for part (a)
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- SOCR Home page: http://www.socr.ucla.edu
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