How can I evaluate the marginal cumulative distribution function of a set of random variables for which I do not have the CDF in closed form. I can, however, simulate from a joint distribution involving this set of variables.
To be more specific, assume I want to evaluate the CDF of (X_1,X_2) but I only have a way to simulate from (X_1,X_2,X_3).
Obviously I can approximate the CDF of (X_1,X_2,X_3) by obtaining a large number of simulations and checking how many observations fall below the desired threshold. But how to get the CDF of (X_1,X_2)?. Can I just simply throw X_3 away and use the same procedure as for the joint PDF?
