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A box contains 6 pens,2 of which are defective. Two pens are taken randomlyfrom the box. If r.v.X, number of defectivepens obtained , then standard deviation |
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Answer» <P>`+-4/(3sqrt(5))` Two pensare takenrandomly from the box. `:.` x can take values `0,1,2` `p(x=0) = (""^(4)C_(2))/(""^(6)C_(2)) = (4 xx3)/(6xx5) = 2/5 = 6/15` `p(x=1) = (""^(2)C_(1)xx""^(4)C_(1))/(""^(6)C_(2)) =(2xx4xx2xx1)/(6xx5)=8/15` `p(x=2)=(""^(2)C_(2))/(""^(6)C_(2)) = (1xx2)/(6xx5) = 1/15` `E(x) = 10/15` and `= 2/3` `E(x^(2)) = 12/15 = 4/5` Standad DEVIATION `= sqrt(E(x^(2)) - [E(x)]^(2))` Standard deviation `=sqrt((4/5)-(2/3)^(2))` `=sqrt(4/5-4/9) =sqrt((36-20)/(45))` `= sqrt((16)/(45)) = 4/(3sqrt(5))` |
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