Home
Class 12
MATHS
Let x1,""x2,"". . . . . . ,""xn be n obs...

Let `x_1,""x_2,"". . . . . . ,""x_n` be n observations, and let ` bar x` be their arithematic mean and `sigma^2` be their variance. Statement 1: Variance of `2x_1,""2x_2,"". . . . . . ,""2x_n""i s""4""sigma^2` . Statement 2: Arithmetic mean of `2x_1,""2x_2,"". . . . . . ,""2x_n""i s""4x` . (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

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.
Promotional Banner

Topper's Solved these Questions

  • STATISTICS

    CENGAGE ENGLISH|Exercise Exercises|39 Videos

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE ENGLISH|Exercise Comprehension Type|6 Videos

  • STRAIGHT LINE

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|8 Videos

Similar Questions

Explore conceptually related problems

Statement 1: sum_(r=0)^n(r+1)^n c_r=(n+2)2^(n-1)dot Statement 2: sum_(r=0)^n(r+1)^n c_r=(1+x)^n+n x(1+x)^(n-1)dot (1) Statement 1 is false, Statement 2 is true. (2) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1 (3) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1. (4) Statement 1 is true, Statement 2 is false.

Consider the function f(x)=|x-2|+|x-5|,x in R . Statement 1: f'(4)=0 Statement 2: f is continuous in [2, 5] , differentiable in (2, 5) and f(2) = f(5) . (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

Let a, b R be such that the function f given by f(x)""=""ln""|x|""+""b x^2+""a x ,""x!=0 has extreme values at x""=""1 and x""=""2 . Statement 1: f has local maximum at x""=""1 and at x""=""2 . Statement 2: a""=1/2"and"b=(-1)/4 (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

Statement 1: The sum of the series 1""+""(1""+""2""+""4)""+""(4""+""6""+""9)""+""(9""+""12""+""16)""+"". . . . . . +""(361""+""380""+""400)"" i s ""8000 . Statement 2: sum_(k=1)^n(k^3-(k-1)^3)=n^3 for any natural number n. (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

Let f(x)""=""x|x|""and""g(x)""=""sinx in x Statement 1 : gof is differentiable at x""=""0 and its derivative is continuous at that point Statement 2: gof is twice differentiable at x""=""0 (1) Statement1 is true, Statement2 is true, Statement2 is a correct explanation for statement1 (2) Statement1 is true, Statement2 is true; Statement2 is not a correct explanation for statement1. (3) Statement1 is true, statement2 is false. (4) Statement1 is false, Statement2 is true

Statement 1: An equation of a common tangent to the parabola y^2=16sqrt(3)x and the ellipse 2x^2+""y^2=""4 ""i s ""y""=""2x""+""2sqrt(3) . Statement 2: If the line y""=""m x""+(4sqrt(3))/m ,(m!=0) is a common tangent to the parabola y^2=""16sqrt(3)x and the ellipse 2x^2+""y^2=""4 , then m satisfies m^4+""2m^2=""24 . (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

Statement -1 (1/2)^7lt(1/3)^4 implies 7log(1/2)lt4log(1/3)implies7lt4 Statement-2 If axltay , where alt0 ,x, ygt0 , then xgty . (a) Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1 Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement -1 (c) Statement -1 is true, Statement -2 is false (d) Statement -1 is false, Statement -2 is true.

Statement-1: The function F(x)=intsin^2xdx satisfies F(x+pi)=F(x),AAxinR ,Statement-2: sin^2(x+pi)=sin^2x (A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True.

Statement-1 : lim_(x to 0) (sqrt(1 - cos 2x))/(x) at (x = 0) does not exist. Statement -2 :Right hand limit != Left hand limit i) Statement - 1 is True, Statement-2 is True, Statement-2 is a correct explanation for statement-1 ii)Statement-1 is True, Statement-2 is True, Statement-2 is Not a correct explanation for statement-1 iii)Statement-1 is True, Statement-2 is False iv)Statement -1 is False, Statement-2 is True

Consider the system of equations x-2y+3z=1;-x+y-2z=; x-3y+4z=1. Statement 1: The system of equations has no solution for k!=3. Statement2: The determinant |1 3-1-1-2k1 4 1|!=0,\ for\ k!=3. Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true