1. ## limiting distrbution

does Gamma function converges in probability? Gamma(n,1/n) n>0
does Gamma function converges in distribution? Gamma(n,1/n) n>0

if yes,find it!

i wanna to use the definition to prove it
but i do not know how to write it

the book gives us the hint:use moment generating function!
but can we use another way to slove?

2. This is not well-posed.
We need to know how the parameters change as n changes.

3. Gamma(n,1/n) n>0

4. IT also makes a difference how you write your gamma density, but I can guess at it via the MGF and calc 2.

Plug into $\left(1-\beta t\right)^{-\alpha}$ and take the limit as n goes to infinity.