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DIRECTIONS: This question contains two statements: statement-1 (Assertion) and statement-2 (Reason). This question also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.
Statement-1: The variance of first n even natural numbers is n² - 1 / 4.
Statement-2: The sum of first n natural numbers is n(n+1)/2 and the sum of squares of first n natural numbers is n(n+1)(2n+1)/6.
- Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1.
- Statement-1 is true, Statement-2 is false.
- Statement-1 is false, Statement-2 is true.
- Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
Correct answer: Statement-1 is false, Statement-2 is true.
Solution
The first n even naturals 2,4,...,2n have mean n+1 and variance = 4*[n(n+1)(2n+1)/6]/n - (n+1)^2 = (n^2 - 1)/3. So Statement-1 is false while Statement-2 (the standard sum formulas) is true.
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