Which of the following can not be valid assignment of probabilities for outcomes of sample space S = {{ω1,ω2,ω3,ω4,ω5,ω6,ω7}
Assignment
ω1
ω2
ω3
ω4
ω5
ω6
ω7
(a)
0.1
0.01
0.05
0.03
0.01
0.2
0.6
(b)
71
71
71
71
71
71
71
(c)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
(d)
-0.1
0.2
0.3
0.4
-0.2
0.1
0.3
(e)
141
142
143
144
145
146
1415
Medium
Open in App
Solution
Verified by Toppr
(a)
ω1
ω2
ω3
ω4
ω5
ω6
ω7
0.1
0.01
0.05
0.03
0.01
0.2
0.6
Here each of the numbers p(ωi) is positive and less than 1 Sum of probabilities =p(ω1)+p(ω2)+p(ω3)+p(ω4)+p(ω5)+p(ω6)+p(ω7) =0.1+0.01+0.05+0.03+0.01+0.2+0.6= 1$$ Thus the assignment is valid (b)
ω1
ω2
ω3
ω4
ω5
ω6
ω7
71
71
71
71
71
71
71
Here each of the number p(ωi) is positive and less than 1 Sum of probabilities = p(ω1)+p(ω2)+p(ω3)+p(ω4)+p(ω5)+p(ω6)+p(ω7) = 71+71+71+71+71+71+71=7×71=1 Thus the assignment is valid (c)
ω1
ω2
ω3
ω4
ω5
ω6
ω7
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Here each of the numbers p(ωi) is positive and less than 1 Sum of probabilities =
p(ω1)+p(ω2)+p(ω3)+p(ω4)+p(ω5)+p(ω6)+p(ω7) =0.1+0.2+0.3+0.4+0.5+0.6+0.7 =2.8=1 Thus the assignment is not valid (d)
ω1
ω2
ω3
ω4
ω5
ω6
ω7
-0.1
0.2
0.3
0.4
-0.2
0.1
0.3
Here p(ω1) and p(ω5) are negative Hence the assignment is not valid (e)