Bound for probability with almost sure convergence
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Let $(X_n)_n$ be random variables which converge almost surely to a constant $x in mathbb R$ , i.e. $X_n xrightarrow{n to infty} x$ a.s. Let $Y$ be another random variable. Question: Can I say something like $$mathrm{Pr}(Y geq X_n) leq mathrm{Pr} left(Y geq frac{x}{2} right)$$ for $n$ large enough?
probability probability-theory convergence stochastic-processes random-variables
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asked Nov 27 at 8:39
Kariani
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