What is Chi-square Probability Distribution?

Answer 1

Given Z~N(0,1), Z^2 follows

χ_1^2 Chi-square Probability Distribution with one degree of freedom

Given Z_i~N(0,1), ∑_(i=1)^ν▒Z_i^2 follows

χ_ν^2 Chi-square Probability Distribution with ν degree of freedom

Given E_ij=n×p_ij=(r_i×c_j)/n, U=∑_(∀i,j)▒(O_ij-E_ij )^2/E_ij follows

χ_((r-1)(c-1))^2 Chi-square Probability Distribution with ν=(r-1)(c-1) degree of freedom

Given E_i=n×p_i, U=∑_(i=1)^m▒(O_i-E_j )^2/E_i follows

χ_(m-1)^2 Chi-square Probability Distribution with ν=m-1 degree of freedom

Answer 2

The Chi-square probability distribution is a probability distribution that describes the distribution of the sum of squared standard normal random variables. It is often used in hypothesis testing and is characterized by its degrees of freedom. The shape of the distribution depends on the degrees of freedom parameter, with larger degrees of freedom resulting in a more symmetric and bell-shaped distribution.