X_1 \sim \Gamma(b_1, p_1)
X_2 \sim \Gamma(b_2, p_2)
Y = c_1X_1 + c_2X_2
M_Y(t) = M_{X_1}(c_1t)M_{X_2}(c_2t) = (1-\frac {c_1t} {b_1})^{-p_1}(1-\frac {c_2t} {b_2})^{-p_2}
Jeśli \displaystyle \alpha = \frac{c_1}{b_1} = \frac{c_2}{b_2}, to \displaystyle Y \sim \Gamma(\frac 1 {\alpha}, p_1+p_2).