1.

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

Answer»

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

Solution :Let x be the number of DEFECTIVEPENS.
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))`


Discussion

No Comment Found

Related InterviewSolutions