ผลต่างระหว่างรุ่นของ "Probstat/week4 practice 2"
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Jittat (คุย | มีส่วนร่วม) (หน้าที่ถูกสร้างด้วย '== Useful properties == 1. For a random variable '''X''' and constants '''a''' and '''c''', prove that '''E[aX+c]=aE[X] + c'''.') |
Jittat (คุย | มีส่วนร่วม) |
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| แถว 1: | แถว 1: | ||
| + | : ''This is part of [[probstat]].'' | ||
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== Useful properties == | == Useful properties == | ||
1. For a random variable '''X''' and constants '''a''' and '''c''', prove that '''E[aX+c]=aE[X] + c'''. | 1. For a random variable '''X''' and constants '''a''' and '''c''', prove that '''E[aX+c]=aE[X] + c'''. | ||
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| + | 2. Let '''X''' be a random variable and <math>\mu={\mathrm E}[X]</math>, prove that <math>{\mathrm E}[X - \mu] = 0</math>. | ||
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| + | == Dinner dish experiment == | ||
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| + | 1. Let | ||
รุ่นแก้ไขเมื่อ 23:51, 10 กันยายน 2557
- This is part of probstat.
Useful properties
1. For a random variable X and constants a and c, prove that E[aX+c]=aE[X] + c.
2. Let X be a random variable and , prove that .
![{\displaystyle \mu ={\mathrm {E} }[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9d988be241dd4f2aba51e76f922ca04363c2956a)
![{\displaystyle {\mathrm {E} }[X-\mu ]=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c91fbd56166a5c0ce17edf3e7be8e0cebc377e8c)
Dinner dish experiment
1. Let
