418531 ภาคต้น 2552/โจทย์ปัญหาความน่าจะเป็น II/เฉลยข้อ 3
ข้อ 1
เราได้ว่า
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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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![{\displaystyle pq\sum _{k=0}^{\infty }[(1-p)(1-q)]^{k}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5e8c0003832e521f9c1b07180eb663669450c0e3) |
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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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ข้อ 2
เนื่องจาก 
ErrorToo many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below.
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พิจารณา เราได้ว่า
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ฉะนั้น
ErrorToo many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below.
![{\displaystyle E[\max(X,Y)]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/07aef3d7becd38298f7e372cc7373ff8cd1c6980) |
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ข้อ 3
เราได้ว่า
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ErrorToo many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below.
![{\displaystyle (1-p)^{k-1}(1-q)^{k-1}{\Big [}p(1-q)+(1-p)q+pq{\Big ]}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fcc5d0f0563cf2fb5e28ba192ea2238971519b6d) |
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ข้อ 4
เราได้ว่า
![{\displaystyle E[X\ |\ X\leq Y]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/86f7a73adcec14351051812682857886468266a9) |
![{\displaystyle E[X\ |\ \min(X,Y)=X]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3de3a633a9d7c80f7579d5eab4dff69824211f87) |
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![{\displaystyle \sum _{k=1}^{\infty }\Pr(\min(X,Y)=k)E[X\ |\ \min(X,Y)=X\wedge \min(X,Y)=k]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/109f01dddaf02b6efa968b4a0a12da9b81277211) |
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ErrorToo many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below.
![{\displaystyle E[\min(X,Y)]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/95992c1022b0df96fe42417e9734e2f99092de06) |
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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 \sum _{k=1}^{\infty }[(1-p)(1-q)]^{k-1}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/79a0cdba10dea6b708b3c7f4de12f0d5fac49f65) |
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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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