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

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

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

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

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

Text Solution

Verified by Experts

The correct Answer is:

(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)`

Topper's Solved these Questions

BINOMIAL DISTRIBUTION
MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Exercise 2 (MISCELLANEOUS PROBLEM) (Mean and Variance|32 Videos
APPLICATIONS OF DERIVATIVES
MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|21 Videos
CIRCLE AND CONICS
MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise All Questions|74 Videos

Let X ~ B (n, p ), if E (X) = 5, Var (X) = 2.5, then P(X<1) is

`(1/2)^11`

`(1/2)^10`

`(1/2)^6`

`(1/2)^9`

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

0.1

0.2

0.5

0.6

For X ~ B (n,p),if E(X) = 18, Var(X) =12, then p =

`1/3`

`2/3`

`3/4`

`1/4`