random variables

Let x and y be random variables, not necessarily independent, that take real values in the interval [0,1]. Let z = xy and let the mean values of x, y, z be x̄, ȳ, z̄, respectively....

Let $ x $ and $ y $ be random variables, not necessarily independent, that take real values in the interval $[0,1]$. Let $ z = xy $ and let the mean values of $ x, y, z $ be $ \bar...

Consider the two statements. S 1 : There exist random variables X and Y such that (E[X - E(X)) (Y - E(Y))]) 2 > Var[X] Var[Y] S 2 : For all random variables X and Y, Cov[X, Y] = E...

Suppose $${X_i}$$ for $$i=1,2,3$$ are independent and identically distributed random variables whose probability mass functions are $$\,\,\Pr \left[ {{X_i} = 0} \right] = \Pr \left...

Let X and Y be two exponentially distributed and independent random variables with mean $$\alpha $$ and $$\beta $$, respectively. If Z = min (X, Y), then the mean of Z is given by