Suppose you are a data scientist working for NASA. You and your team are studying star annihilation. The latest research shows that the probability of star annihilation lasting more than t millon years is

225/(t+15)^2,t>0

After that, the star will rapidly collapse into a black hole.

1. What is the probability density function (PDF) for t? What is the cumulative density function (CDF) for t?

2. Find the probability that a randomly selected star will annihilate within 3 million years.

3. Given that a star has been annihilated for 3 million years already, find the probability that it will annihilate for at least 5 more million years.

4. You observe that a large number of stars begin annihilating today. Find the number of years after which only 10% of these stars are expected to annihilate (the rest have completed annihilation and collapsed into black hole).