Pagina:Teoria degli errori e fondamenti di statistica.djvu/198: differenze tra le versioni
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| || <math> = {\sigma_y}^2 \; \sum\nolimits_i \left[ |
| || <math> = {\sigma_y}^2 \; \sum\nolimits_i \left[ |
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\frac{1}{\Delta} \left( \sum\nolimits_j {x_j}^2 |
\frac{1}{\Delta} \left( \sum\nolimits_j {x_j}^2 - |
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x_i \sum\nolimits_j x_j \right) \right] ^2 </math> |
x_i \sum\nolimits_j x_j \right) \right] ^2 </math> |
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| || <math>= {\sigma_y}^2 \; \sum\nolimits_i \left[ |
| || <math>= {\sigma_y}^2 \; \sum\nolimits_i \left[ |
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\frac{1}{\Delta} \left( N \, x_i - \sum\nolimits_j |
\frac{1}{\Delta} \left( N \, x_i - \sum\nolimits_j |
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x_j \right) \right]</math> |
x_j \right) \right]^2</math> |
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| || <math>= \frac{{\sigma_y}^2}{\Delta^2} \; \sum\nolimits_i \left[ N^2 {x_i}^2 + \left( \sum\nolimits_j x_j \right) ^2 |
| || <math>= \frac{{\sigma_y}^2}{\Delta^2} \; \sum\nolimits_i \left[ N^2 {x_i}^2 + \left( \sum\nolimits_j x_j \right) ^2 |
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Versione attuale delle 08:45, 1 set 2022
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Questa pagina è stata trascritta, formattata e riletta. | |
| 182 | Capitolo 11 - Stime di parametri |
![{\displaystyle ={\sigma _{y}}^{2}\;\sum \nolimits _{i}\left[{\frac {1}{\Delta }}\left(\sum \nolimits _{j}{x_{j}}^{2}-x_{i}\sum \nolimits _{j}x_{j}\right)\right]^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ef1f25495eeea0d3b49f6f6a054ae16d0c3501a2)
![{\displaystyle ={\frac {{\sigma _{y}}^{2}}{\Delta ^{2}}}\;\sum \nolimits _{i}\left[\left(\sum \nolimits _{j}{x_{j}}^{2}\right)^{2}+{x_{i}}^{2}\left(\sum \nolimits _{j}x_{j}\right)^{2}-2\,x_{i}\left(\sum \nolimits _{j}{x_{j}}^{2}\right)\left(\sum \nolimits _{j}x_{j}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/db48869cd0465dd96a600806f4bae0369dcb4ce7)
![{\displaystyle ={\frac {{\sigma _{y}}^{2}}{\Delta ^{2}}}\left[N\left(\sum \nolimits _{j}{x_{j}}^{2}\right)^{2}\!+\left(\sum \nolimits _{i}{x_{i}}^{2}\right)\left(\sum \nolimits _{j}x_{j}\right)^{2}\!-2\left(\sum \nolimits _{j}{x_{j}}^{2}\right)\left(\sum \nolimits _{j}x_{j}\right)^{2}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9fc3420e44b47036ae4e7d00897f062181089b13)
![{\displaystyle ={\frac {{\sigma _{y}}^{2}}{\Delta ^{2}}}\left[N\left(\sum \nolimits _{j}{x_{j}}^{2}\right)^{2}-\left(\sum \nolimits _{j}x_{j}\right)^{2}\left(\sum \nolimits _{j}{x_{j}}^{2}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8d001319afdbfc2112bbf3e2377f444418af76b6)
![{\displaystyle ={\frac {{\sigma _{y}}^{2}}{\Delta ^{2}}}\left(\sum \nolimits _{j}{x_{j}}^{2}\right)\left[N\left(\sum \nolimits _{j}{x_{j}}^{2}\right)-\left(\sum \nolimits _{j}x_{j}\right)^{2}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f727a01117790e62cfe92c806c64177666e91fac)
e, similmente, per :
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![{\displaystyle ={\sigma _{y}}^{2}\;\sum \nolimits _{i}\left[{\frac {1}{\Delta }}\left(N\,x_{i}-\sum \nolimits _{j}x_{j}\right)\right]^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0ccae59801a92821d17dd332affb1d51dfea6ff1)
![{\displaystyle ={\frac {{\sigma _{y}}^{2}}{\Delta ^{2}}}\;\sum \nolimits _{i}\left[N^{2}{x_{i}}^{2}+\left(\sum \nolimits _{j}x_{j}\right)^{2}-2\,N\,x_{i}\sum \nolimits _{j}x_{j}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9885df50dac1d974b0d26f52b9510012c6016ad1)
![{\displaystyle ={\frac {{\sigma _{y}}^{2}}{\Delta ^{2}}}\left[N^{2}\left(\sum \nolimits _{i}{x_{i}}^{2}\right)+N\left(\sum \nolimits _{j}x_{j}\right)^{2}-2\,N\left(\sum \nolimits _{j}x_{j}\right)^{2}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8fd96981de06c5ce531cba62440556835697c1bb)
![{\displaystyle ={\frac {N\,{\sigma _{y}}^{2}}{\Delta ^{2}}}\left[N\left(\sum \nolimits _{i}{x_{i}}^{2}\right)-\left(\sum \nolimits _{j}x_{j}\right)^{2}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b0fb646f65b4814840090e328ac7674285418bf8)
