Fair Dice Please assist me with this problem Let N1 and N2 b

Fair Dice. Please assist me with this problem

Let N1 and N2 be the outcomes of two independent fair dies and let N be defined now by N = N1 + N2 Find the PMF of N. Let N be the outcome of a fair die. Find the probability mass function (PMF) of N.

Solution

The vaues that N can assume are 2,3,4,5,6,7,8,9,10,11,12

The outcomes which gives these values are (1,1), [(1,2),(2,1)],[(2,2),(1,3),(3,1)],...

Hence the PMF is given by

N	2	3	4	5	6	7	8	9	10	11	12
P(N)	1/36	2/36	3/36	4/36	5/36	6/36	5/36	4/36	3/36	2/36	1/36