User StubbornAtom - Mathematics Stack Exchange

26 votes

When not to treat dy/dx as a fraction in single-variable calculus?

answered Aug 28, 2016 at 13:13

17 votes

Convergence of Student's t-distribution to a standard normal

answered May 26, 2019 at 17:06

15 votes

Accepted

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

answered Sep 7, 2017 at 10:33

10 votes

Definite integral over a simplex

answered Jan 24, 2018 at 16:22

10 votes

Accepted

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

answered Aug 21, 2018 at 20:42

10 votes

Accepted

Proof that the sample mean is the "best estimator" for the population mean.

answered Aug 23, 2019 at 15:40

9 votes

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

answered Aug 22, 2016 at 11:59

8 votes

Why does $A^TA=I, \det A=1$ mean $A$ is a rotation matrix?

answered Nov 26, 2016 at 13:08

8 votes

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

answered Nov 11, 2021 at 6:30

7 votes

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

answered Aug 10, 2016 at 7:00

7 votes

Accepted

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

answered Mar 10, 2018 at 17:01

7 votes

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 $N(0,\frac{1}{4})$

answered Feb 12, 2018 at 14:18

7 votes

How should I solve this integral with changing parameters?

answered Mar 9, 2019 at 20:34

6 votes

Accepted

Example of a maximum likelihood estimator that is not a sufficient statistic

answered Dec 20, 2018 at 13:56

6 votes

Is UMVUE unique? Is the best unbiased estimator unique?

answered Mar 26, 2020 at 16:14

6 votes

Express $1 + \frac {1}{2} \binom{n}{1} + \frac {1}{3} \binom{n}{2} + \dotsb + \frac{1}{n + 1}\binom{n}{n}$ in a simplifed form

answered Jul 3, 2016 at 7:17

6 votes

Accepted

The inverse of a Kac-Murdock-Szegő matrix

answered May 21, 2017 at 8:31

6 votes

Accepted

Transforming a matrix to diagonal matrix

answered Sep 23, 2018 at 11:51

6 votes

Accepted

If $X$ and $Y$ are independent $N(0,\sigma^2)$, then $X^2+Y^2$ and $X/Y$ are independent?

answered Oct 17, 2018 at 10:47

6 votes

Accepted

If $m$ tickets are drawn out of $n$ tickets numbered $1$ to $n$, find variance of the sum of the numbers on tickets

answered Jun 11, 2018 at 7:35

6 votes

Accepted

Evaluating $\int_0^\infty\int_0^\infty e^{-(x+y)}\cdot \sin(\frac{\pi\cdot y}{x+y}) \, dy \, dx$

answered Jun 28, 2018 at 16:49

5 votes

Accepted

Minimum mean squared error of an estimator of the variance of the normal distribution

answered Jul 23, 2018 at 14:22

5 votes

How to find $\int_a^bx^mdx$ using the limit sum definition of definite integral?

answered Jul 28, 2018 at 16:31

5 votes

Distribution of range of Uniform $(0,1)$ distribution

answered Jun 25, 2018 at 10:26

5 votes

Accepted

Beta distribution CDF to Binomial Survival Function

answered Oct 14, 2018 at 8:12

5 votes

Accepted

Reciprocal of Expectation

answered Jun 6, 2017 at 16:02

5 votes

Well defined function meaning

answered Nov 18, 2016 at 12:41

5 votes

Constructing a cubic given four points

answered Nov 27, 2016 at 12:53

5 votes

Use $\delta-\epsilon$ to show that $\lim_{n\to\infty} a^{\frac{1}{n}} = 1$?

answered Jul 22, 2016 at 6:50

5 votes

Accepted

If $P \in M_7(\mathbb{R})$ has rank 4, rank of $P + aa^T$, where $a$ is a column vector?

answered Feb 7, 2018 at 20:26

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529 Answers

When not to treat dy/dx as a fraction in single-variable calculus?

Convergence of Student's t-distribution to a standard normal

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

Definite integral over a simplex

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

Proof that the sample mean is the "best estimator" for the population mean.

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

Why does $A^TA=I, \det A=1$ mean $A$ is a rotation matrix?

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

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

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

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 $N(0,\frac{1}{4})$

How should I solve this integral with changing parameters?

Example of a maximum likelihood estimator that is not a sufficient statistic

Is UMVUE unique? Is the best unbiased estimator unique?

Express $1 + \frac {1}{2} \binom{n}{1} + \frac {1}{3} \binom{n}{2} + \dotsb + \frac{1}{n + 1}\binom{n}{n}$ in a simplifed form

The inverse of a Kac-Murdock-Szegő matrix

Transforming a matrix to diagonal matrix

If $X$ and $Y$ are independent $N(0,\sigma^2)$, then $X^2+Y^2$ and $X/Y$ are independent?

If $m$ tickets are drawn out of $n$ tickets numbered $1$ to $n$, find variance of the sum of the numbers on tickets

Evaluating $\int_0^\infty\int_0^\infty e^{-(x+y)}\cdot \sin(\frac{\pi\cdot y}{x+y}) \, dy \, dx$

Minimum mean squared error of an estimator of the variance of the normal distribution

How to find $\int_a^bx^mdx$ using the limit sum definition of definite integral?

Distribution of range of Uniform $(0,1)$ distribution

Beta distribution CDF to Binomial Survival Function

Reciprocal of Expectation

Well defined function meaning

Constructing a cubic given four points

Use $\delta-\epsilon$ to show that $\lim_{n\to\infty} a^{\frac{1}{n}} = 1$?

If $P \in M_7(\mathbb{R})$ has rank 4, rank of $P + aa^T$, where $a$ is a column vector?