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for questions involving inequalities, upper and lower bounds.
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Probabilistic inequality for sum of squares of zero mean Gaussian random variables
Let $X_1,...,X_n$ be i.i.d. standard normal random variables. How to show that there is constant $c>0$ such that for every $a_k>0$ and for every $n>0$: $P(\sum_{k=1}^{n}a_kX_k^2>\sum_{k=1}^{n}a_k+c\cd …