p********0
发帖数: 186 | 1 assume X1 is random variable with N(0, 1) and X2 random variable with N(1,2)
What is the distribution for X3=X1+X2?
Is it a mixture model?? f_(X3) = 1/2 f_{X1) + 1/2 f_{X2} |
d******e
发帖数: 7844 | 2 definitely not.
If X1 and X2 are independent, the sum will be N(1,3)
Btw: This is not called joint distribution
2)
【在 p********0 的大作中提到】
: assume X1 is random variable with N(0, 1) and X2 random variable with N(1,2)
: What is the distribution for X3=X1+X2?
: Is it a mixture model?? f_(X3) = 1/2 f_{X1) + 1/2 f_{X2}
|
p********0
发帖数: 186 | 3 Thanks, Intuitively the answer is correct? How do you prove it?
Through Pdf or moment generation function?
【在 d******e 的大作中提到】
: definitely not.
: If X1 and X2 are independent, the sum will be N(1,3)
: Btw: This is not called joint distribution
:
: 2)
|
z*********o
发帖数: 541 | 4 X3:N(1,3)
2)
【在 p********0 的大作中提到】
: assume X1 is random variable with N(0, 1) and X2 random variable with N(1,2)
: What is the distribution for X3=X1+X2?
: Is it a mixture model?? f_(X3) = 1/2 f_{X1) + 1/2 f_{X2}
|
z*********o
发帖数: 541 | 5 it is a theorem. you can try use mgf
【在 p********0 的大作中提到】
: Thanks, Intuitively the answer is correct? How do you prove it?
: Through Pdf or moment generation function?
|
p********0
发帖数: 186 | 6 Ding
2)
【在 p********0 的大作中提到】
: assume X1 is random variable with N(0, 1) and X2 random variable with N(1,2)
: What is the distribution for X3=X1+X2?
: Is it a mixture model?? f_(X3) = 1/2 f_{X1) + 1/2 f_{X2}
|
c**p
发帖数: 204 | 7 Theory:
X~N(mu1,a1);Y~N(mu2, a2), if independent, then
(X+Y)~ N(mu1+mu2, a1+a2); can extent to n independent ones.
【在 p********0 的大作中提到】
: Thanks, Intuitively the answer is correct? How do you prove it?
: Through Pdf or moment generation function?
|
N**D
发帖数: 10322 | 8 google "sum of normal distributions", go to the result in wiki
2)
【在 p********0 的大作中提到】
: assume X1 is random variable with N(0, 1) and X2 random variable with N(1,2)
: What is the distribution for X3=X1+X2?
: Is it a mixture model?? f_(X3) = 1/2 f_{X1) + 1/2 f_{X2}
|
