CHI SQUARE (χ2)
Definition:
If Z1, ..., Zk are independent, standard normal random variables, then the sum of their squares,
is distributed according to the chi-square distribution with k degrees of freedom.
This is usually denoted as
The chi-square distribution has one parameter: k — a positive integer that specifies the number of degrees of freedom (. the number of Zi’s)
Properties
1. If X 1,X2,…Xn are independent,Xi~N(0,1),(i=1,2,…,n),then
2. If X1,X2,…Xk are independent, Xi~(ni),(i=1,2,…,k),then
3. X1,X2,…Xn are simple random sample from N(,2),then
4.
Probability density function
Cumulative distribution function
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