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A box contains 6 pens, 2 of which are defective, two pens are taken randomly from the box. If r.v.X: number of defective pens obtained, then standard deviation of X= |
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Answer» `+-(4)/(3sqrt(5))` Two pens are taken randomly from the box. `THEREFORE`x and TAKE VALUES 0,1,2 `p(x=0)=(.^(4)C_(2))/(.^(6)C_(2))=(4xx3)/(6xx5)=(2)/(5)=(6)/(15)` `p(x=1)=(.^(2)C_(1)xx.^(4)C_(1))/(.^(6)C_(2))=(2x4xx2xx1)/(6xx5)=(8)/(15)` `p(x=2)=(.^(2)C_(2))/(.^(6)C_(2))=(1x2xx1)/(6xx5)=(1)/(15)` `E(x)=(10)/(15) and =(2)/(3)` `E(x^(2))=(12)/(15)=(4)/(5)` Standard 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((4xx4)/(45))=(4)/(3sqrt(5))` |
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