# Random sample CDF Question

Let http://www.mathhelpforum.com/math-he...276a82d7-1.gif be a random sample from an arbitrary and continuous distribution with cumulative distribution function F(x-http://www.mathhelpforum.com/math-he...c8912759-1.gif). Let http://www.mathhelpforum.com/math-he...d57d6088-1.gif, http://www.mathhelpforum.com/math-he...35769944-1.gif, http://www.mathhelpforum.com/math-he...c7ea0c66-1.gif, $P_4 = P(X_1 + X_2 > 0, X_1 + X_3 >0)$. Now let $W_ij = 1$, if $X_i + X_j > 0$ otherwise $W_ij = 0$. For all distinct h, i, j, k
$E(W_ii) = p_1$,
$Var(W_ii) = p_1 - (p_1)^2$,
$E(W_ij) = p_2$,
$Var(W_ij) = p_1 - (p_2)^2$,
$Cov(W_ij, W_ik) = p_4 - (p_2)^2$,
$Cov(W_ii, W_ik) = p_3 - (p_1)(p_2)$,
$Cov(W_ij, W_hk) = 0$