Two fair dice are to be rolled The total of the spots on the

Two fair dice are to be rolled. The total of the spots on the face-up sides is to be observed. The probability mass function (pmf) of the distribution of X is given as follows: Find sigma x (the standard deviation of the distribution of X). [Note that

Solution

Var(x)=E()-=54.8333-=5.8333

54.8333

x	2	3	4	5	6	7	8	9	10	11	12	Total
p(X=x)	1/36	2/36	3/36	4/36	5/36	6/36	5/36	4/36	3/36	2/36	1/36
p(X=x)	0.03	0.06	0.08	0.11	0.14	0.17	0.14	0.11	0.08	0.06	0.03
E(X)	0.0556	0.1667	0.3333	0.5556	0.8333	1.1667	1.1111	1.0000	0.8333	0.6111	0.3333	7.0000
x*x	4	9	16	25	36	49	64	81	100	121	144
E(x2)	0.1111	0.5000	1.3333	2.7778	5.0000	8.1667	8.8889	9.0000	8.3333	6.7222	4.0000	54.8333