Chi-square with two degrees of freedom
up vote
0
down vote
favorite
How to derive chi-square distribution with $2$ degrees of freedom?
$$X=z_1^2+z_2^2 \
f(z_1,z_2)=frac1{2pi} expleft[frac{-1}{2}(z_1^2+z_2^2)right]$$
Consider the transformation
$$z_1=rcos(theta), qquad z_2=rsin(theta),$$
so that
$$X=z_1^2+z_2^2=r^2cos^2(theta)+r^2sin^2(theta)=r^2.$$
From here I don’t know how to complete.
probability-distributions
edited Nov 24 at 7:50
StubbornAtom
4,89911137
asked Nov 24 at 5:52
Mee Al-Mee
11
add a comment |
up vote
0
down vote
favorite
How to derive chi-square distribution with $2$ degrees of freedom?
$$X=z_1^2+z_2^2 \
f(z_1,z_2)=frac1{2pi} expleft[frac{-1}{2}(z_1^2+z_2^2)right]$$
Consider the transformation
$$z_1=rcos(theta), qquad z_2=rsin(theta),$$
so that
$$X=z_1^2+z_2^2=r^2cos^2(theta)+r^2sin^2(theta)=r^2.$$
From here I don’t know how to complete.
probability-distributions
edited Nov 24 at 7:50
StubbornAtom
4,89911137
asked Nov 24 at 5:52
Mee Al-Mee
11
Where exactly are you stuck? You know how to apply a change of variables. So presumably you know how to complete the process of finding the pdf of $(r,theta)$.
– StubbornAtom
Nov 24 at 7:47
I didn’t know how to complete to find the pdf Could you please help me with is I need to understand the process
– Mee Al-Mee
Nov 24 at 8:52
Do you know the transformation formula that gives you the pdf directly? Do you know jacobians?
– StubbornAtom
Nov 24 at 8:56
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
How to derive chi-square distribution with $2$ degrees of freedom?
$$X=z_1^2+z_2^2 \
f(z_1,z_2)=frac1{2pi} expleft[frac{-1}{2}(z_1^2+z_2^2)right]$$
Consider the transformation
$$z_1=rcos(theta), qquad z_2=rsin(theta),$$
so that
$$X=z_1^2+z_2^2=r^2cos^2(theta)+r^2sin^2(theta)=r^2.$$
From here I don’t know how to complete.
probability-distributions
edited Nov 24 at 7:50
StubbornAtom
4,89911137
asked Nov 24 at 5:52
Mee Al-Mee
11
How to derive chi-square distribution with $2$ degrees of freedom?
$$X=z_1^2+z_2^2 \
f(z_1,z_2)=frac1{2pi} expleft[frac{-1}{2}(z_1^2+z_2^2)right]$$
Consider the transformation
$$z_1=rcos(theta), qquad z_2=rsin(theta),$$
so that
$$X=z_1^2+z_2^2=r^2cos^2(theta)+r^2sin^2(theta)=r^2.$$
From here I don’t know how to complete.
probability-distributions
probability-distributions
edited Nov 24 at 7:50
StubbornAtom
4,89911137
asked Nov 24 at 5:52
Mee Al-Mee
11
edited Nov 24 at 7:50
StubbornAtom
4,89911137
asked Nov 24 at 5:52
Mee Al-Mee
11
edited Nov 24 at 7:50
StubbornAtom
4,89911137
edited Nov 24 at 7:50
StubbornAtom
4,89911137
edited Nov 24 at 7:50
StubbornAtom
4,89911137
4,89911137
asked Nov 24 at 5:52
Mee Al-Mee
11
asked Nov 24 at 5:52
Mee Al-Mee
11
asked Nov 24 at 5:52
Mee Al-Mee
11
11
Where exactly are you stuck? You know how to apply a change of variables. So presumably you know how to complete the process of finding the pdf of $(r,theta)$.
– StubbornAtom
Nov 24 at 7:47
I didn’t know how to complete to find the pdf Could you please help me with is I need to understand the process
– Mee Al-Mee
Nov 24 at 8:52
Do you know the transformation formula that gives you the pdf directly? Do you know jacobians?
– StubbornAtom
Nov 24 at 8:56
add a comment |
Where exactly are you stuck? You know how to apply a change of variables. So presumably you know how to complete the process of finding the pdf of $(r,theta)$.
– StubbornAtom
Nov 24 at 7:47
I didn’t know how to complete to find the pdf Could you please help me with is I need to understand the process
– Mee Al-Mee
Nov 24 at 8:52
Do you know the transformation formula that gives you the pdf directly? Do you know jacobians?
– StubbornAtom
Nov 24 at 8:56
Where exactly are you stuck? You know how to apply a change of variables. So presumably you know how to complete the process of finding the pdf of $(r,theta)$.
– StubbornAtom
Nov 24 at 7:47
Where exactly are you stuck? You know how to apply a change of variables. So presumably you know how to complete the process of finding the pdf of $(r,theta)$.
– StubbornAtom
Nov 24 at 7:47
I didn’t know how to complete to find the pdf Could you please help me with is I need to understand the process
– Mee Al-Mee
Nov 24 at 8:52
I didn’t know how to complete to find the pdf Could you please help me with is I need to understand the process
– Mee Al-Mee
Nov 24 at 8:52
Do you know the transformation formula that gives you the pdf directly? Do you know jacobians?
– StubbornAtom
Nov 24 at 8:56
Do you know the transformation formula that gives you the pdf directly? Do you know jacobians?
– StubbornAtom
Nov 24 at 8:56
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3011240%2fchi-square-with-two-degrees-of-freedom%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Where exactly are you stuck? You know how to apply a change of variables. So presumably you know how to complete the process of finding the pdf of $(r,theta)$.
– StubbornAtom
Nov 24 at 7:47
I didn’t know how to complete to find the pdf Could you please help me with is I need to understand the process
– Mee Al-Mee
Nov 24 at 8:52
Do you know the transformation formula that gives you the pdf directly? Do you know jacobians?
– StubbornAtom
Nov 24 at 8:56