Find the PDF of $U = {XY \over \sqrt{X^2+Y^2}}$ where $X, Y \sim N(0, 1)$ where X,Y are iid RV. Hence find the mean and variance of $U$.
822
Given that $X,Y$ are independent $N(0,1)$ , show that $\frac{XY}{\sqrt{X^2+Y^2}},\frac{X^2-Y^2}{2\sqrt{X^2+Y^2}}$ are independent $N(0,\frac{1}{4})$
84203
Let $X_1$ and $X_2$ are independent $N(0, \sigma^2)$ random variables. What is the distribution of $X_1^2 + X_2^2$?
54731
Derivation of chi-squared pdf with one degree of freedom from normal distribution pdf
25730
Solve $u_x + u_y + u = e^{x+2y}$
1301
Expected value and standard deviation of $X^2$ in terms of moments of $X$
9489
pdf of a product of two independent Uniform random variables
99507
Pdf of the square of a standard normal random variable
59478
MLE of $f(x\vert\theta)=1/\theta$, $x_1 , \cdots , x_n \sim U(0,\theta) \;\;, \theta>0$,
38032
Finding the M.G.F of product of two random variables.
100916
Finding $\mathrm{Cov}(X,Y)$ and $E(X\mid Y=y)$ given the joint density of $(X,Y)$
23476
Derivation of mean and variance of Hypergeometric Distribution
140650
Find the distribution of sum and product of standard normal random variables
6880
Obtain the joint PDF of $\theta_{1} - \theta_{2}$ and $\theta_{1}$ where $\theta_{1}$ and $\theta_{2}$ are i.i.d $\text{Uniform}[0, 2\pi)$
43942
$N(\theta,\theta)$: MLE for a Normal where mean=variance
114953
Find $E[N]$ for $N =\min\{n:U_1+U_2\cdots+U_n>1\}$ where $U_1,U_2, . . .$ are independent uniform (0,1) random variables.
73954
Density function for RV
104431
Mean of a Cauchy Distribution