Show $E(T^r) = e^{r\mu +\frac{r^2 \sigma^2}{2}}$ in a lognormal distribution.
2990
How to compute moments of log normal distribution?
105850
Compute $E(X\mid X+Y)$ for independent random variables $X$ and $Y$ with standard exponential distributions
48686
Show that $e^{-\beta} = \frac{1}{\sqrt{\pi}} \int_{0}^{\infty} \frac{e^{-u}}{\sqrt{u}} e^{-\beta^2 / 4u} du$.
141194
Prove that $\frac{(n-2)s^2}{\sigma^2}\sim \chi^{2}_{n-2}$
103618
Calculate $E(X^{2n})$ where $X$ is normal (0,1)
100801
A $\log \Gamma $ identity: Where does it come from?
32512
lognormal distribution, standard-deviation and (physical) units
125680
Show that $(1+u) \log (1+u) - u \ge \frac{u^2}{2(1+u/3)} $
96180
How to get the derivative of a normal distribution w.r.t its parameters?
36437
How to show that $\log (\frac{2a}{1-a^2}+\frac{2b}{1-b^2}+\frac{2c}{1-c^2})= \log\frac{2a}{1-a^2}+ \log \frac{2b}{1-b^2}+ \log \frac{2c}{1-c^2}$
42193
Show that $E(Y^p)=\int_{0}^{\infty}px^{p-1}P(Y\geq x)dx$
99024
Let $\,E=\{(x,y) \in \Bbb R^2: |x| \le 1,|y|\le 1\}.$
63682
Proving $E[X^4]=3σ^4$
134108
Quantify Difference/Distance between Lognormal distributions
126669
UMVUE of $e^{-\lambda}$ from poisson distribution
35967
Prove the order statistic is a minimal sufficient statistic for the logistic pdf $f(x|\theta)=\frac{e^{-(x-\theta)}}{(1+e^{-(x-\theta)})^2}$
125522
Laplace transform of inverse gaussian distribution