Which of the following cannot be valid assignment of probabilities for outcomes of sample space S = ω1, ω 2, ω 3, ω 4, ω 5, ω 6, ω 7 ? Assignment ω1 ω2 ω3 ω4 ω5 ω6 ω7 (i) 0.1 0.01 0.05 0.03 0.01 0.2 0.6 (ii) (1 / 7) (1 / 7) (1 / 7) (1 / 7) (1 / 7) (1 / 7) (1 / 7) (iii) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 (iv) -0.1 -0.2 -0.3 -0.4 -0.2 -0.1 -0.3 (v) (1 /14) (2 /14) (3 /14) (4/14) (5 /14) (6 /14) (15 /14)

Question

Which of the following cannot be valid assignment of probabilities for outcomes of sample space S = ω1, ω 2, ω 3, ω 4, ω 5, ω 6, ω 7 ? Assignment ω1 ω2 ω3 ω4 ω5 ω6 ω7 (i) 0.1 0.01 0.05 0.03 0.01 0.2 0.6 (ii) (1 / 7) (1 / 7) (1 / 7) (1 / 7) (1 / 7) (1 / 7) (1 / 7) (iii) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 (iv) -0.1 -0.2 -0.3 -0.4 -0.2 -0.1 -0.3 (v) (1 /14) (2 /14) (3 /14) (4/14) (5 /14) (6 /14) (15 /14)  (A) Both (i) and (ii) (B) Both (iii) and (iv) (C) Both (iv) and (v) (D) Only (iii)

Tardigrade Admin · Accepted Answer

(i) Sum of all probabilities = 0.1 + 0.01 + 0 .0 5 + 0.03 + 0 01 + 0 .2 + 0 .6 = 1 Hence, the assignment is valid, as sum is 1 (ii) Valid, as sum is 1 (sam e as part (i)), (iii) Sum of all probabilities = 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0 .6 + 0 .7 = 2.8 Hence, assignment is not valid, as sum is 2.8 > 1. (iv) Not valid, as probabilities of any event can't be negative. (v) Not valid, as (18/7) > 1, which is not possible.

	$ω_{1}$	$ω_{2}$	$ω_{3}$	$ω_{4}$	$ω_{5}$	$ω_{6}$	$ω_{7}$
(i)	$0.1$	$0.01$	$0.05$	$0.03$	$0.01$	$0.2$	$0.6$
(ii)	$\frac{1}{7}$	$\frac{1}{7}$	$\frac{1}{7}$	$\frac{1}{7}$	$\frac{1}{7}$	$\frac{1}{7}$	$\frac{1}{7}$
(iii)	$0.1$	$0.2$	$0.3$	$0.4$	$0.5$	$0.6$	$0.7$
(iv)	$- 0.1$	$- 0.2$	$- 0.3$	$- 0.4$	$- 0.2$	$- 0.1$	$- 0.3$
(v)	$\frac{1}{14}$	$\frac{2}{14}$	$\frac{3}{14}$	$\frac{4}{14}$	$\frac{5}{14}$	$\frac{6}{14}$	$\frac{15}{14}$

Both $(i)$ and $(ii)$

Both $(iii)$ and $(i v)$

Both $(i v)$ and $(v)$

Only $(iii)$