How to set up range for convolution distributions
$begingroup$
I have little difficulty setting up the integration in the beginning,
but have some serious difficulties in setting up the range.
For example, where X~Uniform(0,1) Y~Uniform (0,1)
Z=X+Y
I can understand that z is located between 0 and 2
Which is where everything really goes wrong, because,
based on the above,
I just procceed into convolution like this:
f(z) = (integral -infinity~ infinity) fy(y) fx(z-y) dy
Which obviously goes wrong.
It seems like I need to seperate the integral into two parts
a) where z is located between 0 and 1
b) where z is located betwwen 1 and 2
The first problem : I do not understand why.
Second problem : In cases a, and b, it seems like I need to set up ranges seperately, and they seem to have some kind of relationship with z - meaning just putting 0,1 1,2 on the lower and upper side of the integral isn't enough. I have trouble understanding how to set this up.
I would be grateful if any of you would help.
probability convolution
asked Dec 14 '18 at 14:28
magicmagic
11
$endgroup$
add a comment |
$begingroup$
I have little difficulty setting up the integration in the beginning,
but have some serious difficulties in setting up the range.
For example, where X~Uniform(0,1) Y~Uniform (0,1)
Z=X+Y
I can understand that z is located between 0 and 2
Which is where everything really goes wrong, because,
based on the above,
I just procceed into convolution like this:
f(z) = (integral -infinity~ infinity) fy(y) fx(z-y) dy
Which obviously goes wrong.
It seems like I need to seperate the integral into two parts
a) where z is located between 0 and 1
b) where z is located betwwen 1 and 2
The first problem : I do not understand why.
Second problem : In cases a, and b, it seems like I need to set up ranges seperately, and they seem to have some kind of relationship with z - meaning just putting 0,1 1,2 on the lower and upper side of the integral isn't enough. I have trouble understanding how to set this up.
I would be grateful if any of you would help.
probability convolution
asked Dec 14 '18 at 14:28
magicmagic
11
$endgroup$
add a comment |
$begingroup$
I have little difficulty setting up the integration in the beginning,
but have some serious difficulties in setting up the range.
For example, where X~Uniform(0,1) Y~Uniform (0,1)
Z=X+Y
I can understand that z is located between 0 and 2
Which is where everything really goes wrong, because,
based on the above,
I just procceed into convolution like this:
f(z) = (integral -infinity~ infinity) fy(y) fx(z-y) dy
Which obviously goes wrong.
It seems like I need to seperate the integral into two parts
a) where z is located between 0 and 1
b) where z is located betwwen 1 and 2
The first problem : I do not understand why.
Second problem : In cases a, and b, it seems like I need to set up ranges seperately, and they seem to have some kind of relationship with z - meaning just putting 0,1 1,2 on the lower and upper side of the integral isn't enough. I have trouble understanding how to set this up.
I would be grateful if any of you would help.
probability convolution
asked Dec 14 '18 at 14:28
magicmagic
11
$endgroup$
I have little difficulty setting up the integration in the beginning,
but have some serious difficulties in setting up the range.
For example, where X~Uniform(0,1) Y~Uniform (0,1)
Z=X+Y
I can understand that z is located between 0 and 2
Which is where everything really goes wrong, because,
based on the above,
I just procceed into convolution like this:
f(z) = (integral -infinity~ infinity) fy(y) fx(z-y) dy
Which obviously goes wrong.
It seems like I need to seperate the integral into two parts
a) where z is located between 0 and 1
b) where z is located betwwen 1 and 2
The first problem : I do not understand why.
Second problem : In cases a, and b, it seems like I need to set up ranges seperately, and they seem to have some kind of relationship with z - meaning just putting 0,1 1,2 on the lower and upper side of the integral isn't enough. I have trouble understanding how to set this up.
I would be grateful if any of you would help.
probability convolution
probability convolution
asked Dec 14 '18 at 14:28
magicmagic
11
asked Dec 14 '18 at 14:28
magicmagic
11
asked Dec 14 '18 at 14:28
magicmagic
11
asked Dec 14 '18 at 14:28
magicmagic
11
asked Dec 14 '18 at 14:28
magicmagic
11
11
add a comment |
add a comment |
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