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 Yearling
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Jul
21
awarded  Yearling
Jan
13
comment Philosophers who became mathematicians — how did they do it? And who were they?
As for (4), see another English literature graduate, Reuben Hersh.
Sep
30
awarded  Explainer
Jul
21
awarded  Yearling
Jul
2
awarded  Curious
Jun
10
comment Is it true that $ \mathbb{E}(X\mid X\leq x)\leq \mathbb{E}(X\mid A)$ whenever $\mathbb{P}(X\leq x)\leq \mathbb{P}(A)$?
The fact is true even if $X$'s distribution is not continuous. I'll post my calculation later.
Jun
10
comment Is it true that $ \mathbb{E}(X\mid X\leq x)\leq \mathbb{E}(X\mid A)$ whenever $\mathbb{P}(X\leq x)\leq \mathbb{P}(A)$?
This fact is used in the proof of coherence of CVaR (conditional value at risk) in the Portfolio Analysis lecture notes, and has been stated in above-mentioned generality. The context does not seem to be relevant to the problem.
Jun
10
revised Is it true that $ \mathbb{E}(X\mid X\leq x)\leq \mathbb{E}(X\mid A)$ whenever $\mathbb{P}(X\leq x)\leq \mathbb{P}(A)$?
added forgotten assumption
Jun
10
asked Is it true that $ \mathbb{E}(X\mid X\leq x)\leq \mathbb{E}(X\mid A)$ whenever $\mathbb{P}(X\leq x)\leq \mathbb{P}(A)$?
Dec
18
awarded  Self-Learner
Oct
30
awarded  Taxonomist
Oct
8
awarded  Popular Question
Sep
30
revised What does it mean by $\mathcal{F}$-measurable?
fixed latex
Sep
30
suggested approved edit on What does it mean by $\mathcal{F}$-measurable?
Jul
21
awarded  Yearling
Jun
10
awarded  Fanatic
Jun
3
revised Why is the probability that $(X_1+\ldots+X_n)/n$ converges either $0$ or $1$?
fixed a relevant typo
Jun
3
revised Why is the probability that $(X_1+\ldots+X_n)/n$ converges either $0$ or $1$?
added 35 characters in body
Jun
3
revised Why is the probability that $(X_1+\ldots+X_n)/n$ converges either $0$ or $1$?
added 220 characters in body
Jun
3
revised Why is the probability that $(X_1+\ldots+X_n)/n$ converges either $0$ or $1$?
made title more specific