E2. To be completed after lesson 13

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Exercise 2.1

What is the relationship between a cumulative distribution function (CDF) and a probability density function (PDF)? What is the relationship between as CDF and a probability mass function (PMF)?

Exercise 2.2

How would you expect each of the following to be distributed?

a) The amount of time between repressor-operator binding events.

b) The number of times a repressor binds its operator in a given hour.

c) The amount of time (in total minutes of baseball played) between no-hitters in Major League Baseball.

d) The number of no-hitters in a Major League Baseball season.

e) The winning times of the Belmont Stakes.

To answer this question, try to match these stories to the stories of named distributions. For those of you not familiar with baseball, a no-hitter is a game in which a team concedes no hits to the opposing team. There have only been a few hundred no-hitters in over 200,000 MLB games. The Belmont Stakes is a major horse race that has been run each year for over 150 years.

Exercise 2.3

Write down any questions or points of confusion that you have.