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Dear friends, Is there any known bound on sum of independent but not identically distributed geometric random variables? I have to show that the tail of the sum drops exponentially (like in the Chernoff bounds for the sum of iid geom. variables). Formally, if $X_i$ ~ Geom($p_i$), and $X = \sum_{i=1}^n X_i$, and it is known that $E[X]=\Theta(n)$, Is it possible to show that $\Pr(X < 2E[X]) > 1 - \delta ^n$, where $\delta < 1$? Thank you in advance, Michael. |
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Dear friends, Is there any known bound on sum of independent but not identically distributed geometric random variables? I have to show that the tail of the sum drops exponentially (like in the Chernoff bounds for the sum of iid geom. variables). Formally, if X_i $X_i$ ~ Geom(p_i)Geom($p_i$), and $X = \sum_{i=1}^n X_iX_i$, Is it possible to show that Pr(X $\Pr(X < 2E[X]) > 1 - \delta ^n, n$, where \delta $\delta < 11$? Thank you in advance' , Michael. |
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Probability Theory, Chernoff Bounds, Sum of Independent (but not identically distributed) r.v.Dear friends, Is there any known bound on sum of independent but not identically distributed geometric random variables? I have to show that the tail of the sum drops exponentially (like in the Chernoff bounds for the sum of iid geom. variables). Formally, if X_i ~ Geom(p_i), and X = sum_{i=1}^n X_i, Is it possible to show that Pr(X 1 - \delta ^n, where \delta < 1? Thank you in advance' Michael.
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