query: Show that random variable $U=\frac{X}{X+Y}$ has uniform distribution on [0,1] when X & Y are independent random variables with same exp. distribution.
positive_passages.docid: 26860
positive_passages.text: X,Y are independent exponentially distributed then what is the distribution of X/(X+Y)
negative_passages.docid: 52988
negative_passages.text: Complete Statistic: Uniform distribution
negative_passages.docid: 26833
negative_passages.text: Prove that $\mathbb P(X>Y) =\frac{b}{a + b}$ if $X, Y$ are exponentially distributed with parameters $a$ and $b$.
negative_passages.docid: 156092
negative_passages.text: Existence of independent and identically distributed random variables.
negative_passages.docid: 84785
negative_passages.text: Is $f(x)=x+\frac{x}{x+1}$ uniformly continuous on $(0,\infty)$
negative_passages.docid: 93994
negative_passages.text: Distribution of $\sum_{j=1}^n\ln\left(\frac{X_{(j)}}{X_{(1)}}\right)$ when $X_i$'s are i.i.d Pareto variables
negative_passages.docid: 82279
negative_passages.text: Prove that it is a random variable iff it is constant on each partition
negative_passages.docid: 23603
negative_passages.text: Joint distribution of $X+Y$ and $\frac{X}{X+Y}$
negative_passages.docid: 136707
negative_passages.text: Show that if $X$ and $Y$ are independent with the same exponential distribution, then $Z= |X - Y|$ has the same exponential distribution
negative_passages.docid: 30662
negative_passages.text: $x_{1}...x_{n}$ are independent continuous random variables with common distribution function $F(x)$,compute $E(F(x_{(n)})-F(x_{(1)}))$
negative_passages.docid: 142818
negative_passages.text: X,Y are independent standard normal distributed then what is the distribution of $\frac{X}{X+Y}$
negative_passages.docid: 85955
negative_passages.text: Expected value of maximum of two random variables from uniform distribution
negative_passages.docid: 89186
negative_passages.text: Showing that $\frac{X_{(i)}}{X_{(n)}},i=1,2,...,n-1$ and $X_{(n)}$ are independent for a population with df $F(y)=y^{\theta}$
negative_passages.docid: 152495
negative_passages.text: Prove that if $X$ and $Y$ are Normal and independent random variables, $X+Y$ and $X-Y$ are independent
negative_passages.docid: 114953
negative_passages.text: 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.
negative_passages.docid: 54002
negative_passages.text: Finding the distribution of the sum of three independent uniform random variables
negative_passages.docid: 54769
negative_passages.text: Distribution of sine of uniform random variable on $[0, 2\pi]$