Simulating the binomial variable in Excel and deriving its distribution
This topic is really an important part of introductory Statistics. Exercise 2.2 is designed to model the binomial variable in Excel. As you can notice, sometimes I don't follow my book word-for-word.
- A combination of the Excel commands IF and RAND produces a Bernoulli variable (a coin)
- By definition, the binomial is a sum of coins. I think my definition is the easiest to apply
- To conclude, we give the definition of the coin in a tabular form.
This exercise is a good preparatory step for logical analysis of the binomial variable with three coins.
- Draw a table with four columns: three for the coins and one for their sum.
- Fill out the first line with one realization of coin values (say, three zeros) and their sum.
- Ask the students to fill out the other lines, with all possible combinations of the results for the coins.
- Then draw a new table where the outcomes are grouped by the numbers in the last column. This is the distribution of the binomial variable.
From here you can go to the general case. Mathematically inclined students will need a series of examples to see the importance of the binomial variable.