If you have a story, you can simulate it!

Sometimes, the story describing our probability distribution does not have a named distribution to go along with it. In these cases, fear not! You can always simulate it. We'll do that in this and the next exercise.

In earlier exercises, we looked at the rare event of no-hitters in Major League Baseball. Hitting the cycle is another rare baseball event. When a batter hits the cycle, he gets all four kinds of hits, a single, double, triple, and home run, in a single game. Like no-hitters, this can be modeled as a Poisson process, so the time between hits of the cycle are also Exponentially distributed.

How long must we wait to see both a no-hitter and a batter hit the cycle? The idea is that we have to wait some time for the no-hitter, and then after the no-hitter, we have to wait for hitting the cycle. Stated another way, what is the total waiting time for the arrival of two different Poisson processes? The total waiting time is the time waited for the no-hitter, plus the time waited for the hitting the cycle.

Now, you will write a function to sample out of the distribution described by this story.

Instructions

Define a function with call signature successive_poisson(tau1, tau2, size=1) that samples the waiting time for a no-hitter and a hit of the cycle.
- Draw waiting times tau1 (size number of samples) for the no-hitter out of an exponential distribution and assign to t1.
- Draw waiting times tau2 (size number of samples) for hitting the cycle out of an exponential distribution and assign to t2.
- The function returns the sum of the waiting times for the two events.

Take Hint (-30xp)