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Let x(1),x(2),..,x(n) be n observations,...

Let `x_(1),x_(2),..,x_(n)` be n observations, and let x be their arithmetic mean and `sigma^(2)` be the variance
Statement 1 : Variance of `2x_(1),2x_(2),..,2x_(n) " is" 4sigma^(2)`.
Statement 2: Arithmetic mean `2x_(1),2x_(2),..,2x_(n)` is 4x.

A

Statement 1 is false, statement 2 is true.

B

Statement 1 is true, statement 2 is true, statement 2 is a correct explanation for statement 1.

C

Statement 1 is true, statement 2 is true , statement 2 is not a correct explanation for statement 1.

D

Statement 1 is true, statement 2 is false.

Text Solution

Verified by Experts

The correct Answer is:
D
A.M. of `2x_(1), 2x_(2)..2x_(n) " is" (2x_(1)+2x_(2)+..+2x_(n))/(n)`
`=2((x_(1)+x_(2)+..+x_(n))/(n))=2overline(x)`
So statement 2 is false.
variance `(2x_(i)=2^(2)` variance `(x_(i)=4sigma^(2)`
So statement 1 is true.
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