Question

The mean and variance of two natural number are 3 and 4 respectively. Then Find those numbers​

Answer 1

Answer:





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Class 12

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>>Statement 1: The variance of first n eve

Question



Statement 1: The variance of first n even natural numbers is 4n2−1

Statement 2: The sum of first n natural numbers is 2n(n+1) and the sum of squares of first n natural numbers is 6n(n+1)(2n+1)

A

Statement 1 is true, Statement2 is true,Statement 2 is a correct explanation for Statement 1

B

Statement 1 is true, Statement2 is true;Statement2 is not a correct explanation for statement 1

Your Answer

C

Statement 1 is true, Statement 2 is false.

D

Statement 1 is false, Statement 2 is true

Correct Answer

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Solution



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Correct option is D)

Sum of first n even natural numbers

=2+4+6+...+2n=2(1+2+...+n) 

=22n(n+1)=n(n+1)

Mean (xˉ)=nn(n+1)=n+1

variance =n1(∑x1)2−(xˉ)2=n1(22