How can I show that $E[(\hat\theta -\theta)^2]<Var(\bar X)=\dfrac{1}{n}$?
67489
How to show that $E[(\hat\theta -\theta)^2]<Var(\bar X)=\dfrac{1}{n}$?
36417
Why does $\mathbb{E}(\frac{X_1+...+X_n}{n})=\mathbb{E}(X)$?
359
Show that $\ker \hat{T} = \text{ann}(\text{range } T)$
63388
MLE of uniform distribution on the interval $[\theta − \frac{1}{2}, \theta + \frac{1}{2}]$
62621
Expected value and variance of trace function
19471
Expectation of an absolute value of a normal random variate
6100
Show that $\left|\frac{\alpha - \beta}{1-\bar{\alpha}\beta}\right| < 1$ when $|\alpha|,|\beta| < 1$
69082
Show that $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$
129035
Confidence interval in U(0, $\theta$)
154334
Reference for $\text{Var}(X)\le (b-a)^2/4$
134696
How can I show that the conditional expectation $E(X\mid X)=X$?
93185
asymptotic distribution of $\sqrt{n}(\hat\theta_n-\theta)$ to determine the efficiency of $\hat\theta_n$?
83313
Showing that $\frac{\sqrt[n]{n!}}{n}$ $\rightarrow \frac{1}{e}$
113526
Why intuitively does $\mathbb E(\frac d {d\theta}\log p_\theta(x))=0$?
96722
Finding UMVUE of $\theta$ when the underlying distribution is exponential distribution
104229
Show that $\lim\limits_{y\downarrow 0} y\mathbb{E}[\frac{1}{X};X>y]=0$.
89186
Showing that $\frac{X_{(i)}}{X_{(n)}},i=1,2,...,n-1$ and $X_{(n)}$ are independent for a population with df $F(y)=y^{\theta}$