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Which of the following cannot be valid assignment of probabilities for outcomes of sample Space `S = {omega_1,omega_2,omega_3,omega_4,omega_5,omega_6,omega_7}`

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Concept : for valid assignment , sum of all possibilities of each assignment should be 1 .
(a) sum of all possibilities = `0.1 + 0.01 + 0.05 + 0.03 + 0.01 + 0.2 + 0.6 = 1`
Hence, the assignment is valid .
(b) sum of all possibilities = `1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 = 7/7 = 1`
Hence, the assignment is valid.
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Which of the following cannot be valid assignmentof probabilities for outcomes of sample space S={omega_(1),omega_(2),omega_(3),omega_(4),omega_(5),omega_(6),omega_(7)} ? Assignement omega_(1),omega_(2),omega_(3),omega_(4),omega_(5),omega_(6),omega^(7) a. 0.1,0.01,0.05,0.03,0.01,0.3,0.6 b. 1/7,1/7,1/7,1/7,1/7,1/7,1/7 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. 1/14,2/14,3/14,4/14,5/14,6/14,15/14

Let a sample space be S" "=" "{omega_1,omega_2, .... ,omega_6} . Which of the following assignments of probabilities to each outcome are valid? Outcomes omega_1 omega_2 omega_3 omega_4 omega_5 omega_6 (a) 1/6 1/6 1/6 1/6

Let a sample space be: S={omega_(1),omega_(2),…..omega_(n)} . Which of the following assignments of probability to each outcome are valid? Outcomes omega_(1),omega_(2),omega_(3),omega_(4), omega_(5),omega_(6) a. 1/6,1/6,1/6,1/6,1/6,1/6 b. 1,0,0,0,0,0 c. 1/8,2/3,1/3,1/3,-1/4,-1/3 d. 1/12,1/12,1/6,1/6,1/6,3/2 e. 0.1,0.2,0.3,0.4,0.5,0.6

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det [[1, omega, omega^(2) omega, omega^(2), 1omega^(2), 1, omega]]

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If omega is a complex cube root of unity.Show that Det[[1,omega,omega^(2)omega,omega^(2),1omega^(2),1,omega]]=0

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