418531 ภาคต้น 2552/โจทย์ปัญหาความน่าจะเป็น II/เฉลยข้อ 7
สำหรับ
Too many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below. Too many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below.
Error
Request served via cp5021 cp5021, Varnish XID 667792858
Upstream caches: cp5021 int
Error: 429, Too many requests (f061ab2) at Wed, 13 May 2026 03:45:54 GMTSensitive client information
IP address: 158.108.32.49
Error
Request served via cp5021 cp5021, Varnish XID 688953988
Upstream caches: cp5021 int
Error: 429, Too many requests (f061ab2) at Wed, 13 May 2026 03:45:55 GMTSensitive client information
IP address: 158.108.32.49
ErrorToo many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below.
![{\displaystyle E[X_{i}]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c351ad22dc33eed67b108cbc3330c9e837f50e73) |
ErrorToo many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below.
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![{\displaystyle \Pr(a_{i}<i)E[X_{i}\ |\ a_{i}<i]+\Pr(a_{i}=i)E[X_{i}\ |\ a_{i}=i]+\Pr(a_{i}>i)E[X_{i}\ |\ a_{i}>i]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/406236064de1e0fa6d93713b554e307ab2a74d99) |
ErrorToo many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below.
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ErrorToo many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below.
![{\displaystyle \Pr(a_{i}<i)E[i-a_{i}\ |\ a_{i}<i]+\Pr(a_{i}=i)\cdot 0+\Pr(a_{i}>i)E[a_{i}-i\ |\ a_{i}>i]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3abfe26561cb6a4df99be05f535157234c30a2eb) |
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ErrorToo many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below.
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![{\displaystyle {\frac {i-1}{n}}E[i-a_{i}\ |\ a_{i}<i]+{\frac {n-i}{n}}E[a_{i}-i\ |\ a_{i}>i]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dcf2101084720c5fc7f2f52849cac1435423f2d0) |
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ErrorToo many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below.
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![{\displaystyle {\frac {i-1}{n}}{\big (}i-E[a_{i}\ |\ a_{i}<i]{\big )}+{\frac {n-i}{n}}{\big (}E[a_{i}\ |\ a_{i}>i]-i{\big )}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fb0b6d1d9ac0789026d67379165f82eded770536) |
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ErrorToo many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below.
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ErrorToo many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below.
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ErrorToo many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below.
![{\displaystyle {\frac {1}{2n}}[(i-1)i+(n-i)(n-i+1)]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f6ccf46e0bdaba00889c3b325cbd0c6800b7e7e8) |
ฉะนั้น
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ErrorToo many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below.
![{\displaystyle \sum _{i=1}^{n}{\frac {1}{2n}}[(i-1)i+(n-i)(n-i+1)]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ddc244c41ed3fb1458275a3fc588b99f0e8b6b26) |
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ErrorToo many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below.
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ErrorToo many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below.
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