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comment Let $X,Y$ be random variables in uniform distribution, $0\leq X\leq 3$,$0\leq Y\leq 4$, the probability of $X\leq Y$
Independence? ${}$
Sep
20
comment CDF of two random variables
The exact same question has been asked (and probably deleted some time after) at least three times in the past week under different names. Please stop doing that.
Sep
19
revised Factor theorem for $\bar {\mathcal M}(\mathcal E)^+$ (set of $\mathcal E$-$\mathcal B(\mathbb R)$-measurable functions with values in $[0,\infty]$).
deleted 9 characters in body
Sep
19
comment Factor theorem for $\bar {\mathcal M}(\mathcal E)^+$ (set of $\mathcal E$-$\mathcal B(\mathbb R)$-measurable functions with values in $[0,\infty]$).
You're welcome.
Sep
19
comment Factor theorem for $\bar {\mathcal M}(\mathcal E)^+$ (set of $\mathcal E$-$\mathcal B(\mathbb R)$-measurable functions with values in $[0,\infty]$).
You have defined $\mathcal{E}=\sigma^{-1}(\mathcal{F})$ in your post.
Sep
19
comment Factor theorem for $\bar {\mathcal M}(\mathcal E)^+$ (set of $\mathcal E$-$\mathcal B(\mathbb R)$-measurable functions with values in $[0,\infty]$).
$\sigma^{-1}(\mathcal{F})$ is shorthand notation for $\{\sigma^{-1}(B)\mid B\in\mathcal{F}\}$, thus any set $A\in\sigma^{-1}(\mathcal{F})$ is of the form $\sigma^{-1}(B)$ for some $B\in\mathcal{F}$.
Sep
19
comment function of a random variable problem
What have you tried?
Sep
19
comment Prove $\int s d \mu = \sum^n_{j=1} a_j \mu(A_j)$ for $s=\sum^n_{j=1} a_j 1_{A_j}$ not a standard representation of $s$.
What does non-standard mean? In any case, if you have established linearity of the integral, then it should be straightforward to show.
Sep
19
answered E[X|Y]=E[X] When X and Y are Independent — Proof from Book Question
Sep
19
comment Prove $\int s d \mu = \sum^n_{j=1} a_j \mu(A_j)$ for $s=\sum^n_{j=1} a_j 1_{A_j}$ not a standard representation of $s$.
"I want to prove $\int sd\mu=\sum_k a_j 1_{A_j}$" - Doesn't make sense. The LHS is a real number, the RHS is a function.
Sep
19
answered Factor theorem for $\bar {\mathcal M}(\mathcal E)^+$ (set of $\mathcal E$-$\mathcal B(\mathbb R)$-measurable functions with values in $[0,\infty]$).
Sep
19
comment How to find $E[\sqrt{X}]$ given only a distribution function?
The square-root of a negative number?
Sep
19
comment Well-definedness of the characteristic function of a compound Poisson variable
Of course, thanks for the clarification.
Sep
19
comment Well-definedness of the characteristic function of a compound Poisson variable
But the assumption that $\int \min\{|u|,1|\}\nu(\mathrm du)$ only ensures that $\int_0^1 |u|\nu(\mathrm du)<\infty$ but we need to hold for $\int_0^{2/|t|}$, don't we?
Sep
18
comment Uniform distribution with random support
If A and B follow the same distribution, then the probability of A>B is 0.5 which I wouldn't call improbable.
Sep
18
comment Uniform distribution with random support
How should U(a,b) be interpreted when a>b?
Sep
18
comment A simple question about probability that a r.v. is less than another
@Shash: What? The first formula is nonsense. When X and Y are continuous, the RHS is always zero as pointed out by V.C.
Sep
18
answered Question about the Central Limit Theorem
Sep
18
answered Expectation of a Random Variable multiplied by a Conditonal Expectation.
Sep
16
comment A question involving the probability generating function
First one is correct. For the second, use that $t^{2x}=(t^2)^x$ for any $t$ and $x$.