query: Prove that $X$ and $Z = Y^2$ are independent random variables if X, Y independent
positive_passages.docid: 29339
positive_passages.text: Are functions of independent variables also independent?
negative_passages.docid: 39378
negative_passages.text: Moment generating functions/ Characteristic functions of $X,Y$ factor implies $X,Y$ independent.
negative_passages.docid: 20626
negative_passages.text: Prove that $x^y < y^x$
negative_passages.docid: 95625
negative_passages.text: Variance of product of multiple independent random variables
negative_passages.docid: 38461
negative_passages.text: If random variables are drawn from an identical distribution, why doesn't this guarantee they are independent?
negative_passages.docid: 13831
negative_passages.text: Find $ P(Z>X+Y)$ where $X,Y,Z \sim U(0,1)$ independently
negative_passages.docid: 20728
negative_passages.text: Proof that this is independent
negative_passages.docid: 79457
negative_passages.text: Geometric random variables $X_1:G(p_1)$ $X_2:G(p_2)$ $X_3:G(p_3)$ are independent, prove the following :
negative_passages.docid: 27072
negative_passages.text: If $X_1,X_2$ are independent beta then showing $\sqrt{X_1X_2}$ is beta
negative_passages.docid: 65784
negative_passages.text: If $X,Y$ are independent $\chi ^2$ with $m$ and $n$ degrees of freedom, then $\frac{X}{X+Y} \sim\beta(m/2, n/2)$
negative_passages.docid: 58206
negative_passages.text: Poisson Distribution of sum of two random independent variables $X$, $Y$
negative_passages.docid: 75842
negative_passages.text: Quotient Distribution of Positive Independent Random Variables
negative_passages.docid: 57451
negative_passages.text: Independent variable = Random variable?
negative_passages.docid: 14079
negative_passages.text: On the proof that every positive continuous random variable with the memoryless property is exponentially distributed
negative_passages.docid: 86729
negative_passages.text: Are squares of independent random variables independent?
negative_passages.docid: 138962
negative_passages.text: $X$ is a random variable, if $\Bbb E(X^2)=1$ and $\Bbb E(X)\geq a>0$, prove that $\Bbb P(X\geq\lambda a)\geq(a-\lambda a)^2$ for $0\leq\lambda\leq 1$.
negative_passages.docid: 154309
negative_passages.text: Probability question of independent random varaibles