Let (X,Y) be a bivariate random vector with joint pdf f(x,y). Let U=aX+b
and V=cY+d, where a, b, c and d are fixed constants with a>0 and c>0.
Derive the joint pdf of (U,V).
How to approach this question?
first let X= (U+V)/2 and (U-V)/2 ?
then find Jacobian matrix?
Thanks
Derive the joint pdf...?
2016-07-21 5:22 am
回答 (1)
2016-07-21 7:45 am
U = aX + b ⇔ X = (U - b)/a
V = cY + d ⇔ Y = (V - d)/c
Jacobian = { {1/a, 0}, {0, 1/c} }
|J| = 1/(ac)
g(u, v)
= f( x , y ) |J|
= f[ (u - b)/a , (v - d)/c ] / (ac)
V = cY + d ⇔ Y = (V - d)/c
Jacobian = { {1/a, 0}, {0, 1/c} }
|J| = 1/(ac)
g(u, v)
= f( x , y ) |J|
= f[ (u - b)/a , (v - d)/c ] / (ac)
收錄日期: 2021-04-18 15:19:03
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20160720212224AAwtmrm