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Let x1,x2,……,xn be n observations, and l...

Let `x_1,x_2,……,x_n` be `n observations, and let `barx` be their arithimetic mean and `sigma^2` be their variance.
Statement1: Variance of `2x_1, 2x_2,…..,2x_n` is `4 alpha^2`
Statement2: Arithmetic mean of `2x_1, 2x_2,…..,2x_n` is `4 barx`.

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

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The correct Answer is:
D
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PATHFINDER-STATISTICS AND MATHEMATICAL REASONING-QUESTION BANK
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  2. Which of the following is different from the others?

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  3. In each of the statements pto~q~rtoq and p is true, then

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  4. Additive identity of the Boolean algebra of logical statement is

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  5. Multiplicative identity of the Boolean algebra of logical statements i...

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  6. Let X be a non-empty set, then P(X)={A:AsubX} is a Boolean lattice w.r...

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  7. Which of the following is true?

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  8. Consider the 2-place Boolean function f :{0,1} rarr{0,1} defined by ...

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  9. If x,y are any two elements of a Boolean lattice, then (x'+y')' is equ...

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  10. The mean of the data set comprising of 16 observations is 16 . If one ...

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  11. The variance of first 20 natural numbers is

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  12. The negation of ~svee(~rwedges) is equivalent to

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  13. the variance of first 50 even natural numbers is ,

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  14. The statement ~(pharr~q) is

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  15. All the students of a class perfomed poorly in mathematic. The techer ...

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  16. Statement I : (p^^∼q)∧(∼p^^q) is a fallacy. Statement II : (p→q)↔(∼q→...

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  17. Let x1,x2,……,xn be n observations, and let barx be their arithimetic m...

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  18. The negation of the statement "If I become teacher, then I will open ...

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  19. If the mean deviation about the median of the numbers a, 2a,…50a is 50...

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  20. Consider the following statements P : suman is brilliant, Q: suman ...

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