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Mathematics
Thành Nguyễn's user avatar
Thành Nguyễn's user avatar
Thành Nguyễn's user avatar
Thành Nguyễn
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7
Complete statistic for Normal Distribution $\mathcal{N}(\mu, \mu^2)$
7
Show that if $\frac{S_n - m_n}{s_n} \xrightarrow{d} \mathcal{N}(0, 1)$ with $X_k \sim \text{Ber}(p_k)$ then $\sum_k p_k(1-p_k) = +\infty$
7
Calculate $\sum\limits_{n=0}^{\infty}{\int\limits_{\frac{1}{2}}^{\infty}(1-e^{-t})^{n}e^{-t^2}dt}$
6
How to show $\lim_{t \rightarrow 0^+} \int_0^\infty \dfrac{\sin x}{x + t}dx = \dfrac{\pi}{2}$?
5
How to deduce $ \mathbb{E}(\sqrt{X}) < \infty \implies\int_{\mathbb{R}^+} (1 - F(x))^2 dx < \infty,~X$ being a non-negative integrable rv?