Q.
Which of the following cannot be valid assignment of probabilities for outcomes of sample space
$S = \left\{\omega_{1}, \omega _{2}, \omega _{3}, \omega _{4}, \omega _{5}, \omega _{6}, \omega _{7}\right\}$ ?
Assignment
$\omega_{1}$
$\omega_{2}$
$\omega_{3}$
$\omega_{4}$
$\omega_{5}$
$\omega_{6}$
$\omega_{7}$
(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)$\,\,\,\,$
$\frac{1 }{14}\,\,\,\,$
$\frac{2 }{14}\,\,\,\,$
$\frac{3 }{14}\,\,\,\,$
$\frac{4}{14}\,\,\,\,$
$\frac{5 }{14}\,\,\,\,$
$\frac{6 }{14}\,\,\,\,$
$\frac{15 }{14}\,\,\,\,$
$\omega_{1}$ | $\omega_{2}$ | $\omega_{3}$ | $\omega_{4}$ | $\omega_{5}$ | $\omega_{6}$ | $\omega_{7}$ | |
---|---|---|---|---|---|---|---|
(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)$\,\,\,\,$ | $\frac{1 }{14}\,\,\,\,$ | $\frac{2 }{14}\,\,\,\,$ | $\frac{3 }{14}\,\,\,\,$ | $\frac{4}{14}\,\,\,\,$ | $\frac{5 }{14}\,\,\,\,$ | $\frac{6 }{14}\,\,\,\,$ | $\frac{15 }{14}\,\,\,\,$ |
Probability
Solution: