If $f$ and $g$ are two probability density functions with same support. Do we have $$\int \frac{f}{g} dx \geq 1? $$
For example, in a discrete case, we have positive numbers $(p_1, \cdots, p_n), (q_1, \cdots, q_n)$ such that $\sum p_i =\sum q_i = 1.$ Does the following inequality hold? $$ \sum p_i/q_i \geq n? $$
If so, how to prove? any counterexample if not?