StubbornAtom

Member for 7 years, 5 months
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Kolkata, India

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Score Activity Newest

14

Sign of product of standard normal random variables

Oct 12, 2021

11

Sufficient statistics for Uniform $(-\theta,\theta)$

Jul 7, 2018

10

Why is this estimator biased?

Mar 22, 2019

9

Simple examples of uncorrelated but not independent $X$ and $Y$

Sep 30, 2017

9

Prove that $\mathrm{Cov}(x^TAx,x^TBx) = 2 \mathrm{Tr}(A \Sigma B \Sigma) + 4 \mu^TA \Sigma B \mu$

Jul 12, 2020

Questions

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19

Distribution of $\frac{\sum_{i=1}^n X_iY_i}{\sum_{i=1}^n X_i^2}$ where $X_i,Y_i$s are i.i.d Normal variables

Nov 15, 2018

14

Is $\frac1{n+1}\sum_{i=1}^n(X_i-\overline X)^2$ an admissible estimator for $\sigma^2$?

May 5, 2021

14

Constructing example showing $\mathbb{E}(X^{-1})=(\mathbb{E}(X))^{-1}$

Sep 30, 2017

13

$(2Y-1)\sqrt X\sim\mathcal N(0,1)$ when $X\sim\chi^2_{n-1}$ and $Y\sim\text{Beta}\left(\frac{n}{2}-1,\frac{n}{2}-1\right)$ independently

Feb 8, 2018

12

If $X$ and $Y$ are independent Normal variables each with mean zero, then $\frac{XY}{\sqrt{X^2+Y^2}}$ is also a Normal variable

Mar 13, 2018

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+10

On the existence of UMVUE and choice of estimator of $\theta$ in $\mathcal N(\theta,\theta^2)$ population

+10

Find the UMVUE of $\frac{\mu^2}{\sigma}$ where $X_i\sim\mathsf N(\mu,\sigma^2)$

+10

$T_0$ is MVUE for $\gamma(\theta)$ and $T_1$ is an u.e. for $\gamma(\theta)$ with efficiency 0.0169. Then corr($T_0,T_1$ )?

+10

Prove that $\mathrm{Cov}(x^TAx,x^TBx) = 2 \mathrm{Tr}(A \Sigma B \Sigma) + 4 \mu^TA \Sigma B \mu$

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