Let x1,x2,x3,.....xn be n observations with mean is ¯x and variance is σ2 Statement 1 : The variance of 5x1,5x2,5x3,....,5xnis25σ2 Statement 2 : The mean of 5x1,5x2,.....5xnis10¯x Then which of the following is correct
A
Statement – 1 is true, and Statement – 2 is false
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B
Statement – 1 is false, and Statement – 2 is true
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C
Statement – 1, Statement – 2 are true and Statement – 2 is correct explanation of Statement – 1
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D
Statement – 1, Statement – 2 are true and Statement – 2 is not correct explanation of Statement – 1
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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.