Discrete Random Variables (DRV) - Binomial Probabilities Using Technology

1. Open List & Spreadsheet on a new page.
Name first column 'x' for the number of successes and the second column 'p' for the probability \(p\) associate with each \(x\).

Populate the column of x with the numbers running from 0 to 7 by keying in the formula
seq(n,n,0,7) into the second row of first column.

3. Hit 'enter' and the first column will be filled up with all the x values for the binomial distribution.

4. Key in the formula to calculate probability of each x value in the second row of second column by calling up Binompdf function under: menu > 4: Statistics > 2: Distributions > A: Binomial Pdf.

Fill in the value of n and p in the dialogue box, this p refers to the probability of success of the binomial distribution.
For the x value, you want to use the x from the first column; so click the triangle and select 'x' which represents the value 'x' column.

6. You can scroll down to see all the probabilities associated with each number of success in the binomial distribution \(X \sim B(7,0.35) \).

7. If your n is large and you would like to find the mode quickly, you can convert the table into a probability histogram by: menu > 3: Data > 8: Summary Plot.

8. For the dialogue box, choose 'x' column as X list and Summary List as the 'p' column.
You may choose to display both table and graph together by using 'Split Page'.
It is preferable to have them on separate pages so one can choose 'New Page'.

9. You can confirm that \(x = 2\) has the highest probability and therefore the mode is \(2\).
Take note of the notation used by the GDC, which is \([2.000,3.000]\), that means the horizontal line is equal to \(2\) but not \(3\).