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Let x ₁, x ₂, , x _ n be n observations, and let x be their arithematic mean and ^2 be their variance. Statement 1 : Variance of 2 x₁, 2 x₂, , 2 x_n is 4 ^2 . Statement 2 : Arithmetic mean of 2 x ₁, 2 x ₂, . ., 2 x _ n is 4 x .

Options

  1. AStatement 1 is false, statement 2 is true
  2. BStatement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
  3. CStatement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
  4. DStatement 1 is true, statement 2 is false

Correct answer

D. Statement 1 is true, statement 2 is false

Step-by-step solution

^2= x_i^2 n - ( x_i n )^2 Variance of 2 x₁, 2 x₂, . ., 2 x_n= (2 x_i )^2 n - ( 2 x_i n )^2=4 [ x_i^2 n - ( x_i n )^2 ]=4 ^2 Statement 1 is true. A.M. of 2 x₁, 2 x₂, , 2 x_n= 2 x₁+2 x₂+ +2 x_n n =2 ( x₁+x₂+ +x_n n )=2 x Statement 2 is false.

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