Let (left{X_{n}ight}_{n=1}^{infty}) be a sequence of random variables that converge in distribution to a random variable (X)
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Let \(\left\{X_{n}ight\}_{n=1}^{\infty}\) be a sequence of random variables that converge in distribution to a random variable \(X\) where \(X_{n}\) has distribution function \(F_{n}\) for all \(n \in \mathbb{N}\) and \(X\) has a valid distribution function \(F\). Prove that the sequence \(\left\{X_{n}ight\}_{n=1}^{\infty}\) is bounded in probability.
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