1.

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=

Answer»

`+-(4)/(3sqrt(5))`
`(8)/(3)`
`(16)/(45)`
`(4)/(3sqrt(5))`

Solution :let x be the number of defective pens.
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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