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Let X~B(n,p), if E(X)=5,Var(X)=2.5 then ...

Let `X~B(n,p)`, if E(X)=5,Var(X)`=2.5` then `P(X lt 1)` is equal to

A

`((1)/(2))^(11)`

B

`((1)/(2))^(10)`

C

`((1)/(2))^(6)`

D

`((1)/(2))^(9)`

Text Solution

Verified by Experts

The correct Answer is:
B
(b) Given, mean E(X)=5 and variance, Var (X)`=2.5`
`:." "np=5` and npq`=2.5`
`rArr " " 5q=2.5 rArr q=(1)/(2)`
`:' " "p+q=1`
`p=1-(1)/(2)=(1)/(2)`
Also, `" " np=5`
`:. " " nxx(1)/(2)=5" "`[`:' p=(1)/(2)`]
`rArr " " n=10`
`P(X lt 1)=P(X=0)`
`""^(10)C_(0)((1)/(2))^(0)((1)/(2))^(10-0)`
`=1xx1xx((1)/(2))^(10)=((1)/(2))^(10)`
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