Comment by roughly

The correlation in this case isn't about the distribution for the individual event, it's about the interactions between them - so, for instance, Rent could be anywhere between 1200 and 1800, and Food could be anywhere between 100 and 150, but if Rent is 1200, it means Food is more likely to be 100, and if Food is 150, it means Rent is more likely to be 1800. Basically, there's a shared factor that's influencing both (local cost of living) that's the actual thing you need to model.

So, a realistic modeling isn't 1200~1500 + 100~150, it's (1~1.5)*(1200 + 150) - the "cost of living" distribution applies to both factors.