E5. To be completed after lesson 11

Exercise 5.1

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 5.2

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 5.3

Did you read the solutions to the last homework assignment?

Exercise 5.4

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