Skip to main content

Stack Exchange

StubbornAtom

top accounts reputation activity subscriptions
Top Questions
36 votes

What is the most rigorous definition of a matrix?

linear-algebra matrices definition asked Jun 4, 2016 at 5:33
math.stackexchange.com

22 votes

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

distributions normal-distribution mean mgf asked Nov 15, 2018 at 17:51
stats.stackexchange.com

14 votes

Evaluating $\int _{-100}^{100}\lfloor {x^3}\rfloor \,dx$

calculus integration asked Jul 2, 2016 at 12:05
math.stackexchange.com

14 votes

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

probability distributions random-variable expected-value asked Sep 30, 2017 at 17:59
stats.stackexchange.com

14 votes

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

variance estimators mse decision-theory admissibility asked May 5, 2021 at 19:08
stats.stackexchange.com

13 votes

Distribution and moments of $\frac{X_iX_j}{\sum_{i=1}^n X_i^2}$ when $X_i$'s are i.i.d $N(0,\sigma^2)$

statistics probability-distributions normal-distribution expected-value variance asked Nov 15, 2021 at 14:21
math.stackexchange.com

13 votes

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

self-study distributions mathematical-statistics random-variable asked Feb 8, 2018 at 11:37
stats.stackexchange.com

12 votes

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

self-study distributions mathematical-statistics normal-distribution random-variable asked Mar 13, 2018 at 20:32
stats.stackexchange.com

12 votes

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

mathematical-statistics normal-distribution estimation inference umvue asked Jun 27, 2018 at 15:09
stats.stackexchange.com

12 votes

Validity of confidence interval for $\rho$ when $X\sim N_3(0,\Sigma)$ with $\Sigma_{ij}=\rho^{|i-j|}$

self-study confidence-interval estimation multivariate-analysis multivariate-normal asked Mar 31, 2019 at 12:08
stats.stackexchange.com

1 2 3 4 5 6

Top Answers
26
When not to treat dy/dx as a fraction in single-variable calculus?
math.stackexchange.com

17
Convergence of Student's t-distribution to a standard normal
math.stackexchange.com

15
Find expectation of $\frac{X_1 + \cdots + X_m}{X_1 + \cdots + X_n}$ when $X_1,\ldots,X_n$ are i.i.d
math.stackexchange.com

14
Sign of product of standard normal random variables
stats.stackexchange.com

11
Sufficient statistics for Uniform $(-\theta,\theta)$
stats.stackexchange.com

10
Generate Moments of Continuous Uniform Distribution with Moment Generating Functions
stats.stackexchange.com

10
Definite integral over a simplex
math.stackexchange.com

10
Why is this estimator biased?
stats.stackexchange.com

10
Proof that the sample mean is the "best estimator" for the population mean.
math.stackexchange.com

10
UMVUE of $\frac{\theta}{1+\theta}$ and $\frac{e^{\theta}}{\theta}$ from $U(-\theta,\theta)$ distribution
math.stackexchange.com

9
Finding $\mathbb E(Y_1^2Y_2^2)$ when $(Y_1,Y_2)$ is normal
stats.stackexchange.com

9
Mathematical induction problem: $\frac12\cdot \frac34\cdots\frac{2n-1}{2n}<\frac1{\sqrt{2n}}$
math.stackexchange.com

9
What is the parameter in Spearman's $\rho$
stats.stackexchange.com

9
Prove that $\mathrm{Cov}(x^TAx,x^TBx) = 2 \mathrm{Tr}(A \Sigma B \Sigma) + 4 \mu^TA \Sigma B \mu$
stats.stackexchange.com

9
When can't Cramer-Rao lower bound be reached?
stats.stackexchange.com

9
Find UMVUE of $\frac{1}{\theta}$ where $f_X(x\mid\theta) =\theta(1 +x)^{−(1+\theta)}I_{(0,\infty)}(x)$
stats.stackexchange.com

9
Expectation of truncated normal
stats.stackexchange.com

9
Simple examples of uncorrelated but not independent $X$ and $Y$
stats.stackexchange.com

8
Cramer-Rao lower bound for the variance of unbiased estimators of $\theta = \frac{\mu}{\sigma}$
stats.stackexchange.com

8
Probability that $k$ variables of multivariate Gaussian are positive
stats.stackexchange.com

8
Distribution and moments of $\frac{X_iX_j}{\sum_{i=1}^n X_i^2}$ when $X_i$'s are i.i.d $N(0,\sigma^2)$
math.stackexchange.com

8
How can I calculate $P(X > Y)$?
stats.stackexchange.com

8
Why does $A^TA=I, \det A=1$ mean $A$ is a rotation matrix?
math.stackexchange.com

7
Beta distribution CDF to Binomial Survival Function
math.stackexchange.com

7
Show that, for all $n > 1: \frac{1}{n + 1} < \log(1 + \frac1n) < \frac1n.$
math.stackexchange.com

7
Exponential random variable X with a uniform random variable as its parameter
stats.stackexchange.com

7
How should I solve this integral with changing parameters?
math.stackexchange.com

7
Given that $X,Y$ are independent $N(0,1)$ , show that $\frac{XY}{\sqrt{X^2+Y^2}},\frac{X^2-Y^2}{2\sqrt{X^2+Y^2}}$ are independent $N(0,\frac{1}{4})$
math.stackexchange.com

7
The distribution of the product of a Bernoulli & an exponential random variable
stats.stackexchange.com

7
A question regarding independence of $\min{\{X,Y\}}$ and $X-Y$ when $X,Y$ follows iid geometric distribution
math.stackexchange.com

1 2 3