What are the characteristics of chi-square distribution?

Answer 1

1. Chi-square density curves are right-skewed.

   

Each Chi-square random variable is associated with a degree of freedom (υ),

.

As υ increase, Chi-square curves become more symmetric.

Z2, the square of a normal[0,1] random variable, follows a

distribution.

The sum of 2 independent Chi-square random variables with

υ

1

, υ

2

degrees of freedom respectively, has a Chi-square distribution with

υ = υ

1

+ υ

2

degrees of freedom.

E(

) = υ

and V(

) = 2 υ.

If {X

1

, X

2

, …, Xn} is a random sample of size n drawn from normal population with mean μ and standard deviation σ (i.e., X ~ normal[μ,σ]), then {(n-1)S2 }/ σ2 =

~

.