# Tagged Questions

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### Unbiased estimate $\lambda^2$

Given a Poisson distribution I want to figure out whether $d:(x_1,...,x_n) \mapsto x_1^2$ and $d':(x_1,...,x_n) \mapsto x_1x_2$ are unbiased estimations for $\lambda^2$ ? I mean it would sound ...
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### Proof that a median minimizes 1-norm. [duplicate]

I was wondering whether there is an easy way to show the following: We have a data set $x_1,...,x_n$ and $m$ is a median if for at least half of the n data points we have that $x_i \le m$ and for ...
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### Expectation of $n$-dimensional Inverse Bessel Process

I think the main problem for me is to calculate the integral of $$\int_{0}^{\infty}\frac{e^{-\frac{r^2}{2t}}}{\sqrt{x^2+r^2}}r^{n-1}dr,n\geq2$$ For n=2, change of variable $y=\sqrt{x^2+r^2}$ would ...
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### Stochastic Processes Question

Give an example of a stochastic process $X_{n}$ that is not a Markov chain, such that $P_{y}(N(y)=\infty)=0$ but $E_{y}N(y)=\infty$
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### Are coordinate projections in the Skorokhod space continuous?

I was wondering whether coordinate projections in the Skorokhod space $D[0,1]$ are actually continuous (and, if so, how can this be proven)? many thanks for any comments/ideas. cheers!
I have a question about joint convergence results derived from an FCLT (i.e., a Functional Central Limit Theorem). To motivate my question, consider the following setup: Let $y_t$ be a random walk ...