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Expectation of max of geometric r.v.

Incomplete proof: $$\mathbb{E}X=\int P(X>x) dx$$ so $$\mathbb{E}\max_{1 \leq m \leq n} S_m =\int_0^\infty P\left( \max_{1 \leq m \leq n} S_m > x \right) dx$$ Then we can split up the max using ...
Zoe Allen's user avatar
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Strong law of large numbers for triangular arrays

For verification purpose, I'll also post the complete solution here. For any constant $A > 0$, consider the events $X_{i,n} > nA$ for $i = 1, \dots, n$. By definition, we have $\displaystyle {\...
shark's user avatar
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