Let (U) be a (operatorname{Uniform}(0,1)) random variable and define a sequence of random variables (left{X_{n}ight}_{n=1}^{infty}) as (X_{n}=deltaleft{U

Question:

Let $U$ be a $\operatorname{Uniform}(0,1)$ random variable and define a sequence of random variables $\left\{X_{n}ight\}_{n=1}^{\infty}$ as $X_{n}=\delta\left\{U ;\left(0, n^{-1}ight)ight\}$. Prove that $X_{n} \xrightarrow{p} 0$ as $n ightarrow \infty$.

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