Gamma Random Variable
$\displaystyle S_X=(0,+\infty)$
$\displaystyle f_X(x)=\frac{\lambda(\lambda x)^{\alpha-1}e^{-\lambda x}}{\Gamma(\alpha)}$
감마함수,gamma_function.
$\displaystyle f_X(x)=\frac{\lambda(\lambda x)^{\alpha-1}e^{-\lambda x}}{\Gamma(\alpha)}$
$\displaystyle x>0$ and $\displaystyle \alpha>0, \lambda>0$
여기서 $\displaystyle \Gamma(z)$ 는 감마함수,gamma_function.$\displaystyle E[X]=\alpha/\lambda$
$\displaystyle V[X]=\alpha/\lambda^2$
$\displaystyle V[X]=\alpha/\lambda^2$
감마확률변수의 특별한 경우
- $\displaystyle m-1$ Erlang Random Variable
Erlang_random_variable =,Erlang_random_variable . Erlang_random_variable
{
Erlang Random Variable
Erlang Random Variable
Erlang_random_variable ? 
Erlang_random_variable ? 
Erlang_random_variable ?
Rel. Erlang_distribution =,Erlang_distribution =,Erlang_distribution . Erlang_distribution
} "Erlang Random Variable"
- Chi-Square Random Variable with $\displaystyle k$ degrees of freedom // Chi-Square Random Variable Chi-Square Random Variable
Chi-Square Random Variable