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StubbornAtom's user avatar
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StubbornAtom
  • Member for 7 years, 8 months
  • Last seen this week
  • Kolkata, India
14 votes
Accepted

Sign of product of standard normal random variables

11 votes
Accepted

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

10 votes

Why is this estimator biased?

9 votes
Accepted

Expectation of truncated normal

9 votes

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

9 votes
Accepted

What is the parameter in Spearman's $\rho$

9 votes
Accepted

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

8 votes
Accepted

Probability that $k$ variables of multivariate Gaussian are positive

8 votes
Accepted

Simple Linear Regression: how does $\Sigma\hat{u_i}^2/\sigma^2$ follow chi squared distribution with df (n-2)?

8 votes
Accepted

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

8 votes

When can't Cramer-Rao lower bound be reached?

8 votes
Accepted

Generate Moments of Continuous Uniform Distribution with Moment Generating Functions

7 votes

The distribution of the product of a Bernoulli & an exponential random variable

7 votes

Prove that $\text{Corr}(X^2,Y^2)=\rho^2$ where $X,Y$ are jointly $N(0,1)$ variables with correlation $\rho$

7 votes
Accepted

How can I calculate $P(X > Y)$?

7 votes
Accepted

Exponential random variable X with a uniform random variable as its parameter

7 votes

Finding $\mathbb E(Y_1^2Y_2^2)$ when $(Y_1,Y_2)$ is normal

7 votes
Accepted

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

6 votes
Accepted

Determine the limiting distribution of $n[g(\bar{X}_n)-1/e]$ of iid Poisson samples with two estimators

6 votes

A simple proof for expressing $SSR/\sigma^2$ in simple linear regression as the square of a standard normal

6 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

6 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

6 votes

Find the joint distribution of $X_1$ and $\sum_{i=1}^n X_i$

6 votes
Accepted

UMVU estimator for non-linear transformation of a parameter

6 votes

Is a minimal sufficient statistic also a complete statistic

6 votes
Accepted

Variance of quadratic form for multivariate normal distribution

6 votes
Accepted

Prove that $\frac{(n-2)s^2}{\sigma^2}\sim \chi^{2}_{n-2}$

5 votes
Accepted

Does computing the test statistic for $H_{0}\text{: }\beta = c$, for $c \ne 0$ in a regression require a funky distribution?

5 votes
Accepted

Distribution of $XY$ when $(X,Y) \sim BVN(0,0,1,1,\rho)$

5 votes

Verifying whether $X$ is a complete statistic

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