This is an exercise that I am stuck at. I managed to solve (i) and (ii), which are relatively easy. Here the Feller condition in (i) is as below.
Also, the central limit theorem I learned is like this.
Now, could anyone tell me how to solve the (iii) of the exercise above? I tried to show that the random variables X_n's satisfy the Lindeberg's condition. But, the calculation becomes too complicated...
Also, there is another extra question that when λ is equal or bigger than 1/2, then the sequence (X_n) does not satisfy the Weak Law of Large Numbers. I am stuck at this also. Could anyone please help me with this also?