14.10 Maximum Likelihood Example: Printers

Part I

Suppose that you’ve got a particular sequence of values: \({1, 0, 0, 1, 0, 1, 1, 1, 1, 1}\) that indicate whether a printer any particular time you try to print.

You have data from the last 10 times you tried.

Question:

  • What is the probability (\(p\)) that the printer jams on the next print job?
bbc, office space
bbc, office space

Part II

The data resembles draws from a Bernoulli distribution.

However, even if we want to model this as a Bernoulli distribution, we do not know the value of the parameter, \(p\).

1- Define your random variable.

2- Write down the likelihood function

3- If it will make the math easier, log the likelihood function.

4- Path 1: Maximize the likelihood using calculus

5- Path 2: Maximize using numeric methods.