Question

This question refers to 2.1:

2.8 Using simulation, estimate the number of rolls needed in Exercise until all pos- sible values of X (from 2 to 12) are seen. 2.1 A pair of dice is rolled; let X be the sum of the two numbers that appear Tabulate the pdf for X

Answer 1

A pair of dice is rolled then the sample space is,

	1	2	3	4	5	6
1	(1, 1)	(1, 2)	(1, 3)	(1, 4)	(1, 5)	(1, 6)
2	(2, 1)	(2, 2)	(2, 3)	(2, 4)	(2, 5)	(2, 6)
3	(3, 1)	(3, 2)	(3, 3)	(3, 4)	(3, 5)	(3, 6)
4	(4, 1)	(4, 2)	(4, 3)	(4, 4)	(4, 5)	(4, 6)
5	(5, 1)	(5, 2)	(5, 3)	(5, 4)	(5, 5)	(5, 6)
6	(6, 1)	(6, 2)	(6, 3)	(6, 4)	(6, 5)	(6, 6)

so these 36 outcomes are possible.

Let X be some of two numbers that appear

Thus sum will be from 2 to 12 as

sum={2,3,4,5,6,7,3,4,5,6,7,8,4,5,6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12}

Thus The pdf of X is

X	F	P(X)
2	1	1/36
3	2	1/18
4	3	1/12
5	4	1/9
6	5	5/36
7	6	1/6
8	5	5/36
9	4	1/9
10	3	1/12
11	2	1/18
12	1	1/36
Total	36	1