independent-variables

$X$ and $Y$ are Bernoulli random variables taking values in $\{0,1\}$. The joint probability mass function of the random variables is given by: $$ \begin{aligned} & P(X=0, Y=0)=0.0...

Suppose $X$ and $Y$ are independent and identically distributed random variables that are distributed uniformly in the interval $[0,1]$. The probability that $X \geq Y$ is _______...

Let U and V be two independent zero mean Gaussian random variables of variances $${{1 \over 4}}$$ and $${{1 \over 9}}$$ respectively. The probability $$P(\,3V\, \ge \,\,2U)$$ is

Two independent random variable X and Y are uniformly distributed in the interval [ - 1, 1]. The probability that max [X, Y] is less than 1/2 is

Two independent random variables $$X$$ and $$Y$$ are uniformly distributed in the interval $$\left[ { - 1,1} \right].$$ The probability that max $$\left[ {X,Y} \right]$$ is less th...

Consider two independent random variables $$X$$ and $$Y$$ with identical distributions. The variables $$X$$ and $$Y$$ take values $$0, 1$$ and $$2$$ with probability $$1/2,$$ $$1/4...