9. Consider a simultaneous roll of two dice, and a sample space defined as S fn1;

9. Consider a simultaneous roll of two dice, and a sample space defined as S ¼

fðn1; n2; . . . ; n6Þg, where nj denotes the number of dice showing j dots.

(a) Let X ¼

P6 j¼1 jnj , the total number of dots showing on a roll, and determine the range of X and associated p.d.f., f ðxjÞ.

(b) Develop a graph of the c.d.f. of X: FðxÞ