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A stochastic process is a collection of random variables usually indexed by a totally ordered set.

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Law of large numbers for a sequence of random variables with converging moment

Let $\{X_n\}_{n=1}^\infty$ be a sequence of random variables such that, $$ \forall n,\,\,\mu_n := EX_n < \infty, \quad \mu_n \to \mu < \infty \textrm{ as } n\to\infty. $$ Now for each $n$, let $X_{n …
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