# Gamma Distribution and Transformations

#### aniguchisan

Hi, I have the following question about Gamma Distributions and Transformations. Given the following: It is easy to work out that the MGF of X is: Now, my doubts lie upon the following. Could someone give me a detailed run through these next two questions? As always, any help is greatly appreciated.

#### Anonymous1

Hi, I have the following question about Gamma Distributions and Transformations. Given the following: It is easy to work out that the MGF of X is: Now, my doubts lie upon the following. Could someone give me a detailed run through these next two questions? As always, any help is greatly appreciated.
(a) Multiplicative principle of MGF says:

$$\displaystyle M_Z = M_{X_1}\cdot M_{X_2} = (1-\frac{r}{\beta})^{-\alpha_1}(1-\frac{r}{\beta})^{-\alpha_2} = (1-\frac{r}{\beta})^{-(\alpha_1+\alpha_2)}$$

Uniqueness implies:

$$\displaystyle Z \sim G\Big((\alpha_1+\alpha_2),\beta\Big)$$

#### matheagle

MHF Hall of Honor
I'm not sure what you want.
The instructions are quite explicit.
This is not a difficult problem and it's been solved here several times.

#### Anonymous1

$$\displaystyle \color{red}{\text{Not sure what you want.}}$$
$$\displaystyle \color{red}{\text{The guide is quite explicit.}}$$
$$\displaystyle \color{red}{\text{This has been solved here.}}$$
NOW, it's a Haiku.

• matheagle

#### matheagle

MHF Hall of Honor
if u say so
I'm not an expert on poetry