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1d
comment what is the distribution of a uniform r.v. divided by an exponential r.v.?
Please include what you have tried. Furthermore, without assuming anything about the joint distribution of $(X,Y)$, e.g. independence, nothing can be said about $U$.
1d
comment To show that if T is a Weibull then aT also have a Weibull distribution
Please include your own thoughts. Also, $S(aT)$ is a function on $\Omega$, not on $\mathbb{R}$, so it can't really be a survival function, can it?
1d
reviewed Close Eigenvalues, Eigenvectors, and Invariant Subspaces
2d
comment Check if a given function is a probability density function
What have you tried? What should $f$ satisfy in order to be a density function?
2d
comment Measurability of $\int f(x,\bullet) d\nu$ (product space)
Start by showing it for $f=\mathbf{1}_{C\times D}$ for $C\in A$ and $D\in B$. Then extend to the more general case.
Jul
19
comment let $X$ be a standard Gaussian random variable. Show that $(X,X)$ is not absolutely continuous.
Exactly @Ale! ${}$
Jul
19
comment let $X$ be a standard Gaussian random variable. Show that $(X,X)$ is not absolutely continuous.
I have revised my answer to hopefully it make this more clear.
Jul
19
revised let $X$ be a standard Gaussian random variable. Show that $(X,X)$ is not absolutely continuous.
deleted 444 characters in body
Jul
19
comment let $X$ be a standard Gaussian random variable. Show that $(X,X)$ is not absolutely continuous.
$V=(X,X)$ is a random variable (or vector) with values in $\mathbb{R}^2$ and nothing else. Applying $(1)$ directly yields ${\rm E}[h(V)]=\int_{\mathbb{R}^2} h(v)\,P_V(\mathrm dv)$ and if we assume that $V$ has density $f:\mathbb{R}^2\to\mathbb{R}$ then this is also $\int_{\mathbb{R}^2} h(v)f(v)\,\lambda_2(\mathrm dv)$. You say "and suppose that $V$ is equal to $(X,Y)$". We don't suppose that (there isn't even a $Y$ anywhere). We simply write $v=(x,y)$. Alternatively, you could write $v=(v_1,v_2)$ and obtain $\int_{\mathbb{R}^2} h(v_1,v_2)f(v_1,v_2)\,\lambda_2(\mathrm dv_1,\mathrm dv_2)$.
Jul
19
comment let $X$ be a standard Gaussian random variable. Show that $(X,X)$ is not absolutely continuous.
Isn't that exactly what my answer tries to explain?
Jul
19
answered let $X$ be a standard Gaussian random variable. Show that $(X,X)$ is not absolutely continuous.
Jul
19
comment Proving convergence of events
@Matt: And what would $\lim$ of a set mean?
Jul
18
comment Probability Help! (X,Y) ~ f(x,y) = 8xy $I_D(x,y)$
It's shorthand notation for $f(x,y)=8xy$ when $(x,y)\in D$ and $f(x,y)=0$ otherwise.
Jul
18
comment What is meant here with $\omega _k \in A _j=A_{n_k } $
Then things like $\omega_k\cap A_j$ and $\bigcup_{k>s}\omega_k$ makes no sense.
Jul
18
comment What is meant here with $\omega _k \in A _j=A_{n_k } $
There are some serious notation issues here. Is $\omega_k$ an element or a set?
Jul
17
comment A question on Regular Conditional Probability
Take a look here.
Jul
17
answered A basic question regarding the proof of existence of product measure
Jul
14
comment Notation question: (X,Y) and (Y,X) identically distributed?
Two $n$-dimensional random variables $U$ and $V$ are identically distributed if $P(U\in A)=P(V\in A)$ for all (nice) subsets $A\subseteq\mathbb{R}^n$.
Jul
11
comment Expressing the probability density function of $Ax$ in terms of the pdf of $x$
"as 2 is a valid probability density function on the domain $(0,\infty)$" What?
Jul
3
answered Show $\lim_{n\to\infty}\sqrt{n}\bigg(\frac{\sum_{j=1}^{n}X_j}{\sum_{j=1}^{n}X_j^2}\bigg)=Z$