here is another question i stuck. again if you help me and explain steps, i will be pleased. thanks again

** Suppose that

X1,X2, ,Xnbe i.i.d. random variables with Gamma (α,n) pdf with meanμ=nαand varianceσ^2=αn^2. LetYn→αin probability. Find the limiting distribution of

sqrt(Yn)* [sqrt(sampleXn/nα- 1 ) ]

**

Suppose thatX1, X2,…, Xnare i.i.d. Uniform(0,1). DenoteUn=sqrt(n)*(sampleXn− 1/2) ,n≥1.

Find the moment generating function ofUn.

Find the limiting distributionUnusing first part