Question

We know that in throwing two fair dice independently, the sum of the two outcomes will be 2, 3, …., 12 with respective probabilities I/36, 1/18, 1/12, 1/9, 5/36, 1/6, 5/36, 1/9, 1/12, 1/18, and 1/36. Simulate 1000 independent throws of a pair of independent fair dice, and compare the observed proportion of 2s, ….., 12s with the known probabilities, using an appropriate test from Law Chapter 6. Use a random number function in Excel to generate the 1000 throws. Use the rand() fn in excel to generate the 1000 throws.

Answer 1

Here we need to draw random sample from the discrete uniform distribution with

values 1, 2, 3, 4, 5, and 6 .

So first enter these values in column 1 of excel. Then enter their probabilities in column 2

Step ( 1 ) : Click on Data >>> Data Analysis >>>Random Number Generation>>>OK

Look the following image:

Fill the required information.

THen click on OK

So we get the output with 1000 values in column"C " and "D"

Add them in column "E"

Step 2 ) Using "COUNTIF()" function we need to count the frequencies of 2, 3, ...12

So we get the observed frequencies.

Next find the expected frequencies of 2, 3, ..., 12 by multiplying 1000 to their corresponding probabilities

Next we need to use chi square goodness of feet test :

Complete the columns which are necessary for chisquare test.

See the following image:

The formulae used on the above excelsheet are as follows: