Show that $E[u(X_1)\mid\sum^n_{i=1}X_i=z]=\Phi \left( \frac{\sqrt n(c-z/n)}{\sqrt{n-1}} \right)$
96417
UMVUE for probability of cutoff
28332
Proof of $\frac{(n-1)S^2}{\sigma^2} \sim \chi^2_{n-1}$
138819
Prove that $\phi(n) \geq \sqrt{n}/2$
127291
Show that $\left( \frac{q}{p} \right) \equiv q^{(p-1) / 2} \mod p$, where $\left( \frac{q}{p} \right)$ is the Legendre Symbol
83457
Given the pdf $f(y\mid\theta) = \theta y^{\theta - 1}1_{0<y<1}$, show $E\left(\frac{1}{2\theta\sum_{i = 1}^n W_i}\right) = \frac{1}{2(n-1)}$
147203
How to show that $\lim_{n\to\infty}\left\{f(c+\frac{1}{n^2})+f(c+\frac{2}{n^2})+\cdots+f(c+\frac{n}{n^2})-nf(c)\right\}=\frac{1}{2} f'(c)$
81077
Prove that $E(X^n)^{1/n}$ is non-decreasing for non-negative random variables
37283
Show that $\frac{X-\mu}{\sigma}\sim N(0,1)$ using moment functions
142249
Show that $\lim_{n\to \infty} \int_E \cos^2(nx + a_n) dx = \frac{1}{2}m(E)$
4512
Is there a direct, elementary proof of $n = \sum_{k|n} \phi(k)$?
8913
Show that there is $\xi$ s.t. $f(\xi)=f\left(\xi+\frac{1}{n}\right)$
64844
Finding $E(|X_1|\ |\max |X_i| )$
122769
Show that $\lim_{n\to \infty}\int_{[0,\infty]}\left(1+\dfrac{x}{n}\right)^n\exp(-ax)=\dfrac{1}{a-1}$
57670
Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$
53263
Show $\sum\limits_{d|n}\phi(d) = n$.
137982
Show that $\textbf{ZF}$ shows $\phi$ is $\Delta_1$
83531
Prove $\iint_{x^{2}+y^{2} \leq 1} e^{x^{2}+y^{2}} d x d y \leq\left[\int_{-\frac{\sqrt{\pi}}{2}}^{\frac{\sqrt{\pi}}{2}} e^{x^{2}} d x\right]^{2} $