co - variance 問題

2008-05-04 3:27 am
假設我知道一個直角3角形ABC

斜線AB = 400 米 ( with a standard deviation of 5 毫米 )

內角BAC = 30 度 ( with a standard deviation of 5 seconds {秒} )

AC是橫線,設為 D ( 假設是 horizontal distance )

BC是直線,設為 h ( 假設是 height difference )

而家要你計 variance of D & h 及their co-variance

我宜家知道variance of D 就係18.75002347mm in square

variance of h 就係 6.250070513 mm in square

甘我點樣由variance of D & h 去找出co-variance?

回答 (3)

2008-05-10 5:44 pm
✔ 最佳答案
你應該要用 c = diag { 0.0052 ( 5 / 206265 )2 }
a 同 b 都係 ( 2 x 1 ) matrix
然後就係
co-variance = a T c b
姐係 co-variance = ( 1 x 2 )( 2 x 2 )( 2 x 1)
答案係 : 1 x 1 vector~
參考: 自己計埋落去,我唔想計出來比你
2008-05-05 4:30 am
AB 係 係用機器 measure 出來的數字,是有 measurement error 的
我都唔係好知應該點講
不如我打條Question出來

2008-05-04 20:31:14 補充:
in the following fifgure a total station was placed at point A and measured the distance and vertical angle to target B. The measured distance is 400 m with a standard deviation of 5 mm, and the measured vertical angle is 30 degree with a standard deviation od 5 seconds.

2008-05-04 20:31:23 補充:
From the measurement the horizontal distance , D , and the heu+ight difference, h , between point A & B are computed.
Estimate the variances of the computed D & h and their covariance.

2008-05-05 10:43:34 補充:
係independent
2008-05-05 3:53 am
相信問題冇咁簡單,你講
斜線AB = 400 米 ( with a standard deviation of 5 毫米 )
冇講到distribution,AB是normally distributed? uniform?
AC = AB cos (角BAC), cos一個random variable既distribution係?
AB同角BAC既distribution係唔係independent?
呢d資料都好關鍵。

計Covariance首先要知道Joint distribution,計到先算啦。


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