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Question

Let x1,x2,x3,.....xn be  n  observations with mean is ¯x and variance is σ2
Statement 1 : The variance of 5x1,5x2,5x3,....,5xn is 25σ2
Statement 2 : The mean of 5x1,5x2,.....5xn is 10¯x
Then which of the following is correct


Correct Answer
A
Statement – 1 is true, and Statement – 2 is false
Your Answer
B
Statement – 1 is false, and Statement – 2 is true
Your Answer
C
Statement – 1, Statement – 2 are true and Statement – 2 is correct explanation of Statement – 1
Your Answer
D
Statement – 1, Statement – 2 are true and Statement – 2 is not correct explanation of Statement – 1

Solution

The correct option is A Statement – 1 is true, and Statement – 2 is false
Mean of (5x1,5x2,....5xn)=5x1+5x2+....+5xnn=5¯x
Variance (5x1,5x2,......5xn)=25σ2
Statement – 1 is true and Statement – 2 is false.

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