ผลต่างระหว่างรุ่นของ "Probstat/notes/chi-squared distribution"

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Here we states important properties of the chi-squared distribution without proofs.
 
Here we states important properties of the chi-squared distribution without proofs.
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=== Expectations and variances ===
  
 
If <math>X</math> is chi-squared with <math>n</math> degree of freedom, we have that its expectation
 
If <math>X</math> is chi-squared with <math>n</math> degree of freedom, we have that its expectation
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<math>Var(X) = 2n.</math>
 
<math>Var(X) = 2n.</math>
 
</center>
 
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=== Sample variances ===
  
 
== Links ==
 
== Links ==
 
* [http://en.wikipedia.org/wiki/Chi-squared_distribution Wikipedia article on the chi-squared distribution]
 
* [http://en.wikipedia.org/wiki/Chi-squared_distribution Wikipedia article on the chi-squared distribution]

รุ่นแก้ไขเมื่อ 09:25, 5 ธันวาคม 2557

This is part of probstat.

Definition

Let be independent unit normal random variables. A random variable

is called a chi-squared random variable with degree of freedom. We also write

Wikipedia has a nice article on chi-squared distribution which also includes plots of its pdf and cdf.

Properties

Here we states important properties of the chi-squared distribution without proofs.

Expectations and variances

If is chi-squared with degree of freedom, we have that its expectation

and its variance

Sample variances

Links