Question

Let a random experiment consist of tossing two fair six sided dice. Let x be the minimum number shown on the dice.

Determine the closed form PMF of x.

Hint: Creating a chart for all possible combinations of the two rolls may be helpful.

Answer 1

Solution:

a random experiment consist of tossing two fair six sided dice.Thus its sample space is given by:

x = Minimum number shown on the dice.

Thus sample space for x is given by:

		Die 1
		1	2	3	4	5	6
Die 2	1	1	1	1	1	1	1
	2	1	2	2	2	2	2
	3	1	2	3	3	3	3
	4	1	2	3	4	4	4
	5	1	2	3	4	5	5
	6	1	2	3	4	5	6

Thus possible values of x are: 1,2,3,4,5,6

Now we need to find frequency for each possible outcomes.

Thus we get:

x	Frequency	P(x)
1	11	0.3056
2	9	0.2500
3	7	0.1944
4	5	0.1389
5	3	0.0833
6	1	0.0278
	N = 36

To get P(x) , we divide each frequency by total frequency N = 36

11/36 = 0.3056

9/36 = 0.2500 and so on.

x	P(x)
1	0.3056
2	0.2500
3	0.1944
4	0.1389
5	0.0833
6	0.0278

Thus above table x and P(x) represent the PMF of x.