This problem appears to resemble another one: How many fish are there in a particular lake? As DH notes, just because we may never see all the fish the lake or hear every song in the IRS, it does not automatically mean that we cannot estimate its size. As part of my self-education in Indian logic, I understand this as follows: when we cannot directly perceive and verify (pratyaksha pramaana), we can try to infer this unobserved truth (~anumaana). Sometimes, we can use comparison (~upamaana) to solve this problem. Here are examples of historically significant events in India where estimating unobserved quantities turned out to be important:
1. Estimating the size of native volunteers ready to take on the occupying British Raj as part of 'Operation Red Lotus' in 1857 (covert sampling and proportions)
3. Estimating the size of jute crop in 1930s Bengal (random sampling)
4. The number of civilians killed in the Bengali holocaust of 1943 (random sampling). The blog carries excerpts, but you should read Madhusree Mukerjee's book for an in-depth analysis.
Using the overlapping sample approach and the fish example in DH's book: catch some fish (say 1000), tag them, and let them swim happily around the lake. Again catch fish (say, 1000) and count the proportion of tagged fish (say 5%), indicating that we tagged roughly 5% of all the fish, giving us an estimate of about 20k. We can also calculate, say, a 90% confidence interval for the chosen sample size. Which brings me to the reason for this blog. I noticed that too many songs on the Ilayaraaja radio station offered by Google-music repeated during my office commutes last week. No problem re-listening to Ilayaraaja musical scores like this one (based on Shamukhapriya ragam is my semi-educated guess).
20 songs were mentally tagged on day-1 and released back into the radio station, and 20% of those tagged songs were streamed back to me on day-2. This experiment was repeated a couple of times, yielding similar results, indicating that Google-music's Ilayaraaja station roughly currently stocks about a hundred songs, and I will soon be hearing only repeats.