Diego Fonseca's user avatar
Diego Fonseca's user avatar
Diego Fonseca's user avatar
Diego Fonseca
  • Member for 7 years, 1 month
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9 votes
2 answers
320 views

Let $X_{(1)}\leq X_{(2)}$ be the order statistics. Evaluate $\operatorname{Var}(X_{(j)})$, $\operatorname{Cov}(X_{(1)},X_{(2)})$

5 votes
0 answers
743 views

Find the invariant measure $\pi=(\pi_{1},\pi_{2},\pi_{3})$ for a Markov Chain with transition matrix given

4 votes
2 answers
110 views

What can we say about $N_{i}$ where $N=N_{1}+\cdots+N_{m}$, $N\thicksim Geom(\frac{1-p}{p})$ and conditional distribution of $N_{j}$ is binomial

4 votes
1 answer
470 views

Determine if the following Markov chain is positive recurrent, null recurrent or transcient

3 votes
3 answers
110 views

Calculate $\mathbb{P}[Y=y|X=x]$ where $X$ is the number of claims reported during first year and $Y$ is ultimate number of claims

3 votes
0 answers
558 views

Bootstrap Resampling Vs KDE Resampling

3 votes
0 answers
57 views

Calculate of Lyapunov Exponents of a sequence of random matrices

2 votes
1 answer
82 views

Power of a statistic respect to significance level

2 votes
0 answers
186 views

In the choice of bandwidth for kernel density estimator. Why usually minimize MISE instead of minimizing ISE?

2 votes
1 answer
331 views

If $X\sim \operatorname{lognormal}$ then $Y:=(X-d\mid x\geq d)$ has approximately a Generalized Pareto distribution

1 vote
0 answers
57 views

A Skip Free Negative Random Walk

1 vote
0 answers
27 views

Let $\xi$ random vector and $\zeta^{x}:=x^{T}\xi$ random variable. Is it correct to say that $\int x^{T}y f_{\xi}(y)dy=\int tf_{\zeta^{x}}(t)dt$?

1 vote
1 answer
98 views

Let $\mathbf{R}^{*}$ be rank vector of a random sample and $V=R_{1}^{*}-R_{N}^{*}$. Then $\mathsf{P}(V=k)= \frac{N-|k|}{N(N-1)}$

1 vote
0 answers
60 views

Let $U$ be a $U$-statistic, $\gamma=\mathbb{E}(U)$ and $U^{*}=U-\gamma$. What can we say about Convergence of $\sqrt{n}[U^{*}-\gamma]$?

1 vote
0 answers
78 views

Let $(Y_{n})$ irreducible Markov Chain and $\pi$ invariant measure. Show that if $\pi(0)\neq 0$ then $Y_{n}\cdots Y_{1}Y_{0}$ eventually vanishes

1 vote
0 answers
210 views

What is the intuition behind loss functions in regression? Can I create one? What rules should I follow?

0 votes
0 answers
37 views

Calculate the transition matrix of $X_{n+1}:= \sum_{i=0}^{X_{n}}\theta_{n}^{i}\:\: \mbox{mod }5.$ where $\theta_{n}^{i}\sim Bin(3,1/3)$ i.i.d

0 votes
0 answers
32 views

Let $(X_{1},\ldots,X_{N})\overset{d}{=}(Y_{1},\ldots,Y_{N})$. Show that $P(X_{1}<\cdots <X_{N})=P(Y_{1}<\cdots <Y_{N})$

0 votes
0 answers
21 views

Seeking Lower Bound for Partition Probability in Random Variable Analysis

-1 votes
1 answer
87 views

Let $X$ and $Y$ random variables, $\{X_{i}\}_{i=1}^{n}$, and $\{Y_{i}\}_{i=1}^{n}$ samples. Is $\{(X_{1},Y_{1})\}_{i=1}^{n}$ a sample of $Z=(X,Y)$? [closed]