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3h
comment Lebesgue-Stieltjes Measure associated to $F$.
The Lebesgue-Stieltjes measure associated to $F$ is the unique Borel measure $\mu_F$ satisfying $\mu_F((a,b])=F(b)-F(a)$ for all $a<b$. Now, to show the properties stated in Problem 28 you need to invoke some basic properties of measures. For instance, to find $\mu_F([a,b])$ you need to write $[a,b]$ in terms of intervals of the form $(a_n,b_n]$ and then use the basic properties to evaluate.
6h
comment Proof of floor function identity.
If $l+1>x$ isn't the case, then we must have $l+1\leqslant x$, but this contradicts the definition of $l$.
7h
comment Lebesgue-Stieltjes Measure associated to $F$.
What's the question?
1d
awarded  Enlightened
1d
awarded  Nice Answer
2d
answered Splitting an integral
2d
answered Showing $\sum_{n\in\mathbb{N}}\int{|f_{n}-f|d\mu}<\infty$ implies $f_{n}\rightarrow f$ almost everywhere.
Jan
27
reviewed Looks OK The center and centralizer of a group.
Jan
26
comment Is it true that E [ X | E [ X | Y] ] = Ex [ X | Y] ? Does this law have a name?
But what's the significance of the subscript, i.e. why not just write $E[Z(Y)]$ as is commonly done?
Jan
26
comment Is it true that E [ X | E [ X | Y] ] = Ex [ X | Y] ? Does this law have a name?
What's with the subscripts?
Jan
22
comment Proof of Wald's Identity, is this valid?
How do you justify the first equality?
Jan
20
answered Show that $S(f^{-1}(C))=f^{-1}(S(C))$
Jan
20
comment Minimizing Expected Value
A density doesn't have to exist.
Jan
20
comment Minimizing Expected Value
Correct. What's holding you back then?
Jan
20
comment Minimizing Expected Value
How do you usually minimize a differentiable function?
Jan
13
answered Show that the variance is biased
Jan
13
comment Derive the distribution of a lower censored s.v.
Did you want to write that $Y=X$ if $X\geqslant b$ and $Y=0$ if $X<b$? As it is written now, the definition of Y doesn't make sense.
Jan
7
comment Cumulative Distribution Functions of random variable is a random variable
Show that every monotone function is Borel measurable.
Dec
20
awarded  Constituent
Dec
19
comment $\mathbb E[\bar X_n]=0$
aka the tower property for conditional expectations.