Question

An experiment involves rolling three dice and recording the sum. a) calculate the probability of each sum b) verify that the sum of the probability is 1

Answer 1

blow is the pmf of X (sum of all three rolls)

P(X=3)=P(all three rolls shows a 1) =(1/6)*(1/6)*(!/6)=1/216

P(X=4)=P(1 roll shows a 2 and other two shows 1)=3*(1/6)*(!/6)*(1/6)=3/216

P(X=5)=P(2 shows a 1 and other 3)+P(two shows a 2 and other 1)=(6/216)

P(X=6)=10/216

P(X=7)=15/216

P(X=8)=21/216

P(X=9)=25/216

P(X=10)=27/216

P(X=11)=27/216

P(X=12)=25/216

P(X=13)=21/216

P(X=14)=15/216

P(X=15)=10/216

P(X=16)=6/216

P(X=17)=3/216

P(X=18)=1/216

sum of above probabilities =(1/216)*(1+3+6+10+15+21+25+27+27+25+21+15+10+6+3+1)=1