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if X~B(n,p) with n=10,p=0.4, then E(X^(2...

if `X~B(n,p)` with `n=10,p=0.4`, then `E(X^(2))=`

A

4

B

2.4

C

3.6

D

18.4

Text Solution

Verified by Experts

The correct Answer is:
D
given, `n=10 and p=0.4`
`thereforeq=1-p=1-0.4=0.6`
`E(x)=np=10(0.4)=4`
`sigma^(2)=npq=10(0.4)(0.6)=2.4`
We know that,
`sigma^(2)=E(X^(2))-(E(X))^(2)`
`E(X^(2))=sigma^(2)+(E(X))^(2)`
`impliesE(X^(2))=2.4+(4)^(2)=2.4+16=18.4`
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