## Random Sample from CDF

Let $X_1,X_2,......,X_n$ be a random sample from an arbitrary and continuous distribution with cumulative distribution function F(x- $\theta$). Let $p_1 = P(X_1 > 0)$, $p_2 = P(X_1 + X_2> 0)$, $p_3 = P(X_1 + X_2> 0, X_1 > 0)$. Show that, when then the population is symmetric at zero and is continunous, $P_3$ = 3/8