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Mathematics
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chuck
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A PhD student in social science trying to learn maths.

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4
A step involving integration by part in a proof
Jul 29, 2019
3
Show that if $E(X_n|\mathcal{F}_n)\rightarrow_p 0$ then $X_n\rightarrow_p 0$.
Apr 30
3
Proving inequality (induction?)
Apr 9, 2021
3
Let $Y_n,X_n$ be a sequence of r.v. Does $\sup_z \Big|P(Y_n<z\ |\ X_n) - \Phi(z)\Big|\rightarrow_p0 \implies \{Y_n|X_n=x_n\}\xrightarrow[]{d}N(0,1)?$
Jan 2, 2022
3
Two different definitions of Lebesgue Integral in Royden
Mar 29, 2021
3
Fatou's lemma - Royden's proof
Mar 26, 2021
2
Some basic set theory proofs.
Jun 7, 2015
2
If $X_n>0$ and $X_n\uparrow X$ with $E(X)<\infty$, then $E(X_n|\mathcal{F})\uparrow E(X|\mathcal{F})$.
Mar 26, 2023
2
Bounded function, monotonic function and infimum
Nov 2, 2016
2
Let $X_n,Y_n$ be two sequences of random variable, where $0<X_n<Y_n$. Does $Y_n=O_p(1)$ imply $X_n=O_p(1)?$
Jan 9, 2022