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?
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.