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Aug
17
comment Proof of the properties of limits of CDFs
@BuckCherry Why should they equate? The LHS is 1 while the RHS depends on some mysterious $n$.
Aug
10
reviewed Looks OK Root of Logarithmic Equation
Aug
10
comment Show that Var$(XY|Y) = Y^2$Var$(X|Y)$
It relies on the following property of conditional expectations: $\mathrm{E}[UV\mid \mathcal{G}]=U\mathrm{E}[V\mid\mathcal{G}]$ if $U$ is $\mathcal{G}$-measurable.
Aug
7
comment Why does $[X\in A]=[(X, Y)\in A\times \mathbb R]$
"the other a set of ordered pairs." - No it isn't. $[(X,Y)\in A\times \mathbb{R}]=\{\omega\in\Omega\mid (X(\omega),Y(\omega))\in A\times\mathbb{R}\}$.
Aug
6
comment What does it mean to integrate with respect to the distribution function?
@DahnJahn: Yep, it's just two ways of writing the same thing. Usually, one would write $\int f(x)\,\mu(\mathrm dx)$ or $\int f(x)\, \mathrm d\mu(x)$ to make the integration variable explicit. Otherwise, one writes $\int f\,\mathrm d\mu$.
Aug
6
comment What does it mean to integrate with respect to the distribution function?
@DahnJahn: As a Lebesgue integral.
Aug
5
comment One-parameter distribution used in survival analysis
The gamma distribution.
Aug
5
comment Inferring total probability knowing conditional probabilities and basic probabilities
Absolutely. ${}$
Aug
5
comment Inferring total probability knowing conditional probabilities and basic probabilities
Hint: $I=\bigcup\limits_{j=1}^n I\cap T_j$, where the latter are disjoint sets.
Jul
22
awarded  Nice Answer
Jul
20
comment Expectation with exponential random variable
@Chival: $\mathrm{E}[Y\mid A]=\mathrm{E}[Y\mathbf{1}_A]/P(A)$ for any event $A$ with $P(A)>0$. Hence you have an indicator function too much.
Jul
20
comment Expectation with exponential random variable
@Math1000: It is a number, since we're conditioning on a set, not a sigma-algebra.
Jul
17
answered Deriving density of a function of a random variable
Jul
17
answered Splitting the summation sign
Jul
17
answered Why Does $\rm{E}[1_A \mid X] = P^X(A\mid X)$?
Jul
15
comment On the central limit theorem
You're right, it doesn't make sense since the righthand side depends on $n$.
Jul
15
comment Plugging a random variable into a probability function?
What definition of $\mathbb{E}(X\mid Z)$ are you working with?
Jul
15
revised What's the name of this theorem?
added 19 characters in body
Jul
15
revised What's the name of this theorem?
added 51 characters in body
Jul
15
comment What's the name of this theorem?
@Ant: You need some kind of topological structure in order to talk about open sets and continuity. I have never heard this theorem go under any name by itself, but it's a consequence of the uniqueness of densities which again is a consequence of the uniqueness theorem of measures.