====== Wnioskowanie Statystyczne - Lista 3. ======
===== Zadanie 1. =====

$X_1 \sim \Gamma(b_1, p_1)$

$X_2 \sim \Gamma(b_2, p_2)$

$Y = c_1X_1 + c_2X_2$

$M_Y(t) = M_{X_1}(c_1t)M_{X_2}(c_2t) = (1-\frac {c_1t} {b_1})^{-p_1}(1-\frac {c_2t} {b_2})^{-p_2}$

Jeśli $\displaystyle \alpha = \frac{c_1}{b_1} = \frac{c_2}{b_2}$, to $\displaystyle Y \sim \Gamma(\frac 1 {\alpha}, p_1+p_2)$.

===== Zadanie 2. =====
===== Zadanie 3. =====
===== Zadanie 4. =====
===== Zadanie 5. =====
===== Zadanie 6. =====
===== Zadanie 7. =====
===== Zadanie 8. =====
===== Zadanie 9. =====
===== Zadanie 10. =====


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