Question

Which of the following can not be valid assignment of probabilities for outcomes of sample space S =

Assignment	ω1	ω2	ω3	ω4	ω5	ω6	ω7
(a)	0.1	0.01	0.05	0.03	0.01	0.2	0.6
(b)
(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)

Answer 1

(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(ω_i) is positive and less than 1.

Sum of probabilities

Thus, the assignment is valid.

(b)

ω1	ω2	ω3	ω4	ω5	ω6	ω7

Here, each of the numbers p(ω_i) is positive and less than 1.

Sum of probabilities

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(ω_i) is positive and less than 1.

Sum of probabilities

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)

ω1	ω2	ω3	ω4	ω5	ω6	ω7

Here,

Hence, the assignment is not valid.