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 Jun 19 comment Is it possible to have $\mathbb E S_n \to \infty$ but $\inf S_n = -\infty$ a.s.? @ByronSchmuland Yeah, you're right about case 1. It should be $S_n = 0$ for all $n$. Jun 19 asked Is it possible to have $\mathbb E S_n \to \infty$ but $\inf S_n = -\infty$ a.s.? Jun 18 accepted Sum of positive i.i.d. random variables. Jun 18 asked Sum of positive i.i.d. random variables. Jun 17 comment How many ways can $5$ rings be placed on $4$ fingers? Shouldn't this goes to infinity? Jun 16 comment combinatorics - Distribution of Distinct Balls into Distinct Boxes By nPk do you mean $\binom n k$? Jun 16 accepted Convergence to exponential function. Jun 14 revised $X,Y$ i.i.d., $X$ and $(X+Y)/\sqrt{2}$ have the same dist., then show that $X$ has a normal distribution deleted 2 characters in body Jun 14 answered $X,Y$ i.i.d., $X$ and $(X+Y)/\sqrt{2}$ have the same dist., then show that $X$ has a normal distribution Jun 13 revised Convergence to exponential function. added 39 characters in body Jun 13 asked Convergence to exponential function. Jun 3 accepted Scheffe’s Theorem Jun 3 comment Scheffe’s Theorem @ChrisJanjigian I see, it is $1 \le n \le \infty$. Thanks! Jun 3 comment Scheffe’s Theorem @ChrisJanjigian How do we get $\int f_\infty = 1$? Dominated convergence theorem? Jun 3 asked Scheffe’s Theorem May 31 comment Difference between $P(Y \ge y)$ and $P(Y > y)$. Thanks! Somehow I believed the sum should starts from $0$ without much thinking. May 30 accepted Difference between $P(Y \ge y)$ and $P(Y > y)$. May 30 comment Difference between $P(Y \ge y)$ and $P(Y > y)$. As for the sum, I was thinking if $>$ and $\ge$ versions of Lemma 2.2.8 is equivalent. Then we should have $\mathbb E(Y) = \int_0^\infty P (Y \ge y) \, \mathrm dy = \sum_{y \ge 0} P(Y \ge y)$, for $Y$ takes only integer values which seems to be wrong. May 30 comment Difference between $P(Y \ge y)$ and $P(Y > y)$. So actually we can replace $>$ with $\ge$ in the proof? I'm confused because latter in the book, exercise 2.2.7, a generalized version of Lemma 2.2.8 is given, with $>$ replaced by $\ge$, that's why I'm considering whether there are difference between the two. May 30 comment Difference between $P(Y \ge y)$ and $P(Y > y)$. But the integral $\int_0^\infty py^{p-1} 1_{(Y > y)} \, \mathrm dy$ should not change if we replace $>$ with $\ge$, right? This is an integral with respect to Lebesgue measure, which shouldn't change when omitting a single point.