Lesson 9 exercises

Exercise 9.1

What is the relationship between a cumulative distribution function (CDF) and a probability density function (PDF)? We didn’t cover it in class, but what is the relationship between as CDF and a probability mass function (PMF)?

Exercise 9.2

Say I am interested in modeling the time it takes for a certain process to happen in a cell. For reasons that you will understand in future lessons, we might model the time \(t\) to be Exponentially distributed, having probability density function

\begin{align} f(t) = \beta \mathrm{e}^{-\beta t}. \end{align}

  1. Write down the CDF, \(F(t)\).

  2. Say you are interested instead in the reciprocal time, \(k = 1/t\). Write down the PDF for \(k\).

Exercise 9.3

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