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Which of the following can not 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)}` Assignment `omega_(1)" "omega_(2)" "omega_(3)" "omega_(4)" "omega_(5)" "omega_(6)`
(a) `0.1` `0.01` `0.05` `0.03` `0.01` `0.2` `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`

Text Solution

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The correct Answer is:
(a) Yes, (b) Yes, (c) No, (d) No, (e) No.
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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)} ?

Let a sample space be S = {omega-(1), omega_(2),....,omega_(6)} . Which of the following assingments of probabilities to each outcomes 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) 0.6 0.6 0.6 0.6 0.6 0.6 .

Knowledge Check

  • If omega ne 1" and "omega^(3)=1 , the (a omega+b + c omega^(2))/(a omega^(2)+b omega+c)+(a omega^(2)+b+c omega)/(a+b omega+c omega^(2)) is equal to

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    B
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    C
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    D
    `2omega^(2)`

  • If omega = cis (2pi)/(3) , then the number of distinct roots of |(z+1, omega, omega^(2)),(omega, z+ omega^(2), 1),(omega^(2) ,1, z+ omega)|=0

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  • If omega = cis (2pi)/(3) , then number of distinct roots of |(z+1,omega,omega^(2)),(omega,z + omega^(2),1),(omega^(2),1,z+omega)| = 0.

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