Let \(\left\{X_{n}ight\}_{n=1}^{\infty}\) be a sequence of independent random variables where \(X_{n}\) has probability distribution function

\[f_{n}(x)= \begin{cases}1-n^{-\alpha} & x=0 \\ n^{-\alpha} & x=n \\ 0 & \text { otherwise }\end{cases}\]

and \(0<\alpha<1\). Prove that there does not exist a random variable \(Y\) such that \(P\left(\left|X_{n}ight| \leq|Y|ight)=1\) for all \(n \in \mathbb{N}\) and \(E(|Y|)<\infty\).